https://script.spoken-tutorial.org/index.php?action=history&feed=atom&title=Python-3.4.3%2FC3%2FAdvanced-Matrix-Operations%2FEnglish 2026-05-14T00:49:39Z Revision history for this page on the wiki MediaWiki 1.23.17 https://script.spoken-tutorial.org/index.php?title=Python-3.4.3/C3/Advanced-Matrix-Operations/English&diff=45230&oldid=prev 2018-12-07T13:07:49Z

<p></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 13:07, 7 December 2018</td> </tr><tr><td colspan="2" class="diff-lineno">Line 205:</td> <td colspan="2" class="diff-lineno">Line 205:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Slide Assignment 2: Infinity norm</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Slide Assignment 2: Infinity norm</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Find the infinity norm of the <del class="diffchange diffchange-inline">matrix </del>'''im.'''</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Find the <ins class="diffchange diffchange-inline">'''</ins>infinity norm<ins class="diffchange diffchange-inline">''' </ins>of the '''<ins class="diffchange diffchange-inline">matrix&#160; </ins>im.'''</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr> <tr><td colspan="2" class="diff-lineno">Line 257:</td> <td colspan="2" class="diff-lineno">Line 257:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>We have unpacked these values into <del class="diffchange diffchange-inline">variable </del>'''U, sigma''' and '''V''''' underscore '''''conjugate.'''</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>We have unpacked these values into '''<ins class="diffchange diffchange-inline">variable </ins>U, sigma''' and '''V''''' underscore '''''conjugate.'''</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr> <tr><td colspan="2" class="diff-lineno">Line 303:</td> <td colspan="2" class="diff-lineno">Line 303:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''smat''' is a 2 by 3 zero matrix</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''smat''' is a 2 by 3 <ins class="diffchange diffchange-inline">'''</ins>zero matrix<ins class="diffchange diffchange-inline">'''</ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr> <tr><td colspan="2" class="diff-lineno">Line 328:</td> <td colspan="2" class="diff-lineno">Line 328:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>It means elements in '''m1''' and in product of''' U, sigma '''and''' V''''' underscore '''''conjugate '''are equal.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>It means <ins class="diffchange diffchange-inline">'''</ins>elements<ins class="diffchange diffchange-inline">''' </ins>in '''m1''' and in product of''' U, sigma '''and''' V''''' underscore '''''conjugate '''are equal.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr> </table>

Nancyvarkey https://script.spoken-tutorial.org/index.php?title=Python-3.4.3/C3/Advanced-Matrix-Operations/English&diff=45140&oldid=prev 2018-11-21T05:36:57Z

<p></p> <a href="https://script.spoken-tutorial.org/index.php?title=Python-3.4.3/C3/Advanced-Matrix-Operations/English&amp;diff=45140&amp;oldid=45048">Show changes</a>

Nancyvarkey https://script.spoken-tutorial.org/index.php?title=Python-3.4.3/C3/Advanced-Matrix-Operations/English&diff=45048&oldid=prev 2018-11-08T07:37:56Z

<p></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 07:37, 8 November 2018</td> </tr><tr><td colspan="2" class="diff-lineno">Line 191:</td> <td colspan="2" class="diff-lineno">Line 191:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>We changed value of element at row 0 column 1 and row 1 column 3 to 0.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>We changed <ins class="diffchange diffchange-inline">the </ins>value of element at row 0 column 1 and row 1 column 3 to 0.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr> <tr><td colspan="2" class="diff-lineno">Line 294:</td> <td colspan="2" class="diff-lineno">Line 294:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>We have unpacked these <del class="diffchange diffchange-inline">value </del>into variable '''U''', '''sigma''' and '''V''''' underscore '''''conjugate.'''</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>We have unpacked these <ins class="diffchange diffchange-inline">values </ins>into variable '''U''', '''sigma''' and '''V''''' underscore '''''conjugate.'''</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td colspan="2" class="diff-lineno">Line 367:</td> <td colspan="2" class="diff-lineno">Line 367:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''smat''' is a '''2 '''by''' 3''' matrix created for multiplication by placing values of '''sigma''' as diagonal elements and <del class="diffchange diffchange-inline">'''</del>zero elsewhere<del class="diffchange diffchange-inline">'''</del>.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''smat''' is a '''2 '''by''' 3''' matrix created for multiplication by placing values of '''sigma''' as diagonal elements and zero elsewhere.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> </table>

Nirmala Venkat https://script.spoken-tutorial.org/index.php?title=Python-3.4.3/C3/Advanced-Matrix-Operations/English&diff=45045&oldid=prev 2018-11-08T05:33:31Z

<p>Created page with &quot;&#039;&#039;&#039;Title of script&#039;&#039;&#039;: &#039;&#039;&#039;Advanced Matrix Operations&#039;&#039;&#039; &#039;&#039;&#039;Author: Puneeth, Thirumalesh H S, Arun KP&#039;&#039;&#039; &#039;&#039;&#039;Keywords: Python, IPython, array, matrices, norm, svd, video tutor...&quot;</p> <p><b>New page</b></p><div>'''Title of script''': '''Advanced Matrix Operations'''<br /> <br /> '''Author: Puneeth, Thirumalesh H S, Arun KP'''<br /> <br /> '''Keywords: Python, IPython, array, matrices, norm, svd, video tutorial'''<br /> <br /> <br /> {| style=&quot;border-spacing:0;&quot;<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| &lt;center&gt;'''Visual Cue '''&lt;/center&gt;<br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| &lt;center&gt;'''Narration'''&lt;/center&gt;<br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Show Slide title<br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Welcome to the spoken tutorial on '''Advanced matrix operations'''. <br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Show Slide <br /> <br /> Objectives <br /> <br /> <br /> <br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| In this tutorial, you will learn to, <br /> <br /> * find''' Frobenius''' and '''infinity''' '''norm''' of a '''matrix'''<br /> * find '''singular value decomposition''' of a '''matrix'''.<br /> <br /> <br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Show Slide <br /> <br /> System Specifications <br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| To record this tutorial, I am using <br /> <br /> * '''Ubuntu Linux 16.04''' operating system<br /> * '''Python 3.4.3 '''and<br /> * '''IPython 5.1.0'''<br /> <br /> <br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Show Slide <br /> <br /> Pre-requisites <br /> <br /> <br /> <br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| To practise this tutorial, you should know about<br /> <br /> * '''Lists, arrays '''and '''accessing parts of arrays '''and<br /> * performing''' '''basic''' matrix operations'''<br /> <br /> If not, see the relevant Python tutorials on this website.<br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Show Slide<br /> <br /> <br /> '''flatten()'''<br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| First we will see about '''flatten''' function.<br /> <br /> * '''flatten() '''function returns a copy of the array collapsed into one dimension.<br /> * It''' '''can be used to convert a '''multidimensional matrix''' into a '''single''' '''dimension matrix'''<br /> <br /> <br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Open '''terminal'''<br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Let us start '''ipython'''. <br /> <br /> <br /> Open the '''terminal.'''<br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Type,<br /> <br /> '''ipython3 '''<br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Type, '''ipython3 '''and press '''Enter'''.<br /> <br /> <br /> From here onwards remember to press the Enter key after typing every command on the terminal.<br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Type,<br /> <br /> '''from numpy import asmatrix,arange'''<br /> <br /> <br /> '''a = asmatrix(arange(1,10).reshape(3,3))'''<br /> <br /> <br /> '''a'''<br /> <br /> <br /> '''a.flatten()'''<br /> <br /> <br /> Highlight '''numpy import asmatrix,arange'''<br /> <br /> <br /> Highlight '''(arange(1,10).reshape(3,3))'''<br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Now let us see how to create '''arrays'''<br /> <br /> <br /> Type<br /> <br /> '''from numpy import asmatrix,arange'''<br /> <br /> <br /> '''a''''' is equal to''''' asmatrix '''''inside brackets''''' arange '''''inside brackets '''''1''''' comma '''''10''''' dot '''''reshape '''''inside brackets '''''3 '''''comma '''''3'''<br /> <br /> <br /> Then type, '''a'''<br /> <br /> <br /> Now type, '''a''''' dot '''''flatten''''' open and close brackets''<br /> <br /> <br /> First we imported''' arange''' function from '''numpy''' module.<br /> <br /> <br /> Here, we can see '''3 by 3''' matrix is converted into one dimensional matrix.<br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Show Slide<br /> <br /> '''Frobenius norm''' of a '''matrix'''<br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Next we will see about '''frobenius norm.'''<br /> <br /> * It is defined as the [http://mathworld.wolfram.com/SquareRoot.html square root] of the sum of the absolute squares of its elements.<br /> <br /> <br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| <br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Pause the video.<br /> <br /> <br /> Try this exercise and then resume the video.<br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Show Slide<br /> <br /> Assignment 1: '''Frobenius''' '''norm''' <br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Find out the '''Frobenius''' '''norm''' of the '''inverse''' of the given 4 by 4 '''matrix'''.<br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Switch to terminal<br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Switch back to the terminal for the solution.<br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Type,<br /> <br /> '''m = asmatrix(arange(1,17).reshape(4,4))'''<br /> <br /> <br /> Highlight asmatrix(arange(1,17).reshape(4,4))<br /> <br /> <br /> Type,<br /> <br /> '''&lt;nowiki&gt;m[0,1] = 0&lt;/nowiki&gt;'''<br /> <br /> '''&lt;nowiki&gt;m[1,&lt;/nowiki&gt;3] =0'''<br /> <br /> <br /> '''m'''<br /> <br /> <br /> <br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Type<br /> <br /> '''m '''''is equal to''''' asmatrix '''''inside brackets''''' arange '''''inside brackets '''''1''''' comma '''''17 '''''dot '''''reshape '''''inside brackets '''''4''''' comma '''''4'''<br /> <br /> <br /> Here, we have used '''asmatrix, arange''' and '''reshape''' functions.<br /> <br /> <br /> We created a matrix of size 4 by 4 containing elements from 1 to 16.<br /> <br /> <br /> Now type,<br /> <br /> '''m '''''inside square brackets '''''0 '''''comma '''''1''''' is equal to''''' 0'''<br /> <br /> '''m '''''inside square brackets '''''1''''' comma '''''3 '''''is equal to''''' 0'''<br /> <br /> <br /> Then type, '''m'''<br /> <br /> <br /> We changed value of element at row 0 column 1 and row 1 column 3 to 0.<br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Type,<br /> <br /> '''from numpy.linalg import inv, norm'''<br /> <br /> '''im = inv(m)'''<br /> <br /> '''norm(im)'''<br /> <br /> <br /> Highlight numpy.linalg import inv, norm<br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| In order to find out the '''Frobenius''' '''norm''' of the inverse of '''matrix''' '''m''', type as shown.<br /> <br /> <br /> '''norm''' function is available in''' numpy.linalg '''module<br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Show Slide<br /> <br /> '''Infinity norm'''<br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Next, we will see about infinity '''norm''' of a '''matrix.'''<br /> <br /> <br /> It is defined as the maximum value of sum of the '''absolute''' value of '''elements''' in each row.<br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| <br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Pause the video.<br /> <br /> <br /> Try this exercise and then resume the video.<br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Slide Assignment 2: Infinity norm<br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Find the infinity norm of the matrix '''im.'''<br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Switch to terminal<br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Switch back to the terminal for the solution.<br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Type,<br /> <br /> '''from numpy import infnorm(im,ord=inf)'''<br /> <br /> <br /> <br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| To find out the '''Infinity''' '''norm''' of the '''matrix''' '''im''', type as shown.<br /> <br /> <br /> Here value for '''ord''' parameter is passed as '''inf''' to calculate '''infinity norm'''.<br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Type, '''norm?'''<br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| To know more about '''norms''' type '''norm '''''question mark''<br /> <br /> <br /> Press '''q''' to exit.<br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Show Slide<br /> <br /> '''Singular value decomposition'''<br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Next we will see about '''singular value decomposition.'''<br /> <br /> <br /> In&amp;nbsp;[https://en.wikipedia.org/wiki/Linear_algebra linear algebra], <br /> <br /> * the&amp;nbsp;'''singular value decomposition'''&amp;nbsp;is factorization&amp;nbsp;of '''real'''&amp;nbsp;or&amp;nbsp;'''complex&amp;nbsp;matrix.'''&lt;br/&gt; <br /> <br /> <br /> <br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Type,<br /> <br /> '''from numpy import matrix'''<br /> <br /> '''from numpy.linalg import svd'''<br /> <br /> '''&lt;nowiki&gt;m1 = matrix([[3,2,2],[2,3,-2]])&lt;/nowiki&gt;'''<br /> <br /> '''U,sigma,V_conjugate = svd(m1)'''<br /> <br /> <br /> Type,<br /> <br /> '''U'''<br /> <br /> '''sigma'''<br /> <br /> '''V_conjugate'''<br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| The SVD of '''matrix''' m1 can be found using '''svd '''function available in the '''numpy.linalg '''module.<br /> <br /> <br /> Type as shown.<br /> <br /> <br /> '''svd''' returns a tuple of 3 elements. <br /> <br /> <br /> We have unpacked these value into variable '''U''', '''sigma''' and '''V''''' underscore '''''conjugate.'''<br /> <br /> <br /> Type, Capital '''U'''<br /> <br /> <br /> Type,''' sigma'''<br /> <br /> <br /> Type, Capital '''V''''' underscore '''''conjugate'''<br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Type,<br /> <br /> '''from numpy import diag,allclose'''<br /> <br /> '''from numpy.matlib import zeros'''<br /> <br /> '''smat = zeros((2,3))'''<br /> <br /> <br /> '''smat'''<br /> <br /> <br /> '''&lt;nowiki&gt;smat[:2, :2] = diag(sigma)&lt;/nowiki&gt;'''<br /> <br /> <br /> Type,<br /> <br /> '''smat'''<br /> <br /> <br /> Type,<br /> <br /> '''allclose(m1, U * smat * V_conjugate)'''<br /> <br /> <br /> <br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| We can validate the singular value decomposition by comparing the product of: <br /> <br /> '''U''', '''sigma''' and '''V '''''underscore '''''conjugate '''with''' m1'''<br /> <br /> <br /> '''sigma''' is a one dimensional array which contains only the diagonal elements of the matrix. <br /> <br /> <br /> Type as shown.<br /> <br /> <br /> We first convert this array to a matrix. <br /> <br /> <br /> Type,<br /> <br /> '''smat'''<br /> <br /> <br /> '''smat''' is a 2 by 3 zero matrix<br /> <br /> <br /> Now type,<br /> <br /> '''smat''''' inside square brackets colon '''''2 '''''comma''''' '''''colon '''''2 '''''is equal to''''' diag '''''inside brackets '''''sigma'''<br /> <br /> <br /> Then type,<br /> <br /> '''smat'''<br /> <br /> <br /> This replaces values at row 0 column 0 and row 1 column 1 in '''smat '''with values from '''sigma. '''<br /> <br /> <br /> '''smat''' is a '''2 '''by''' 3''' matrix created for multiplication by placing values of '''sigma''' as diagonal elements and '''zero elsewhere'''.<br /> <br /> <br /> Type as shown.<br /> <br /> <br /> It returns '''True'''.<br /> <br /> <br /> It means elements in '''m1''' and in product of''' U, sigma '''and''' V''''' underscore '''''conjugate '''are equal.<br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Show Slide<br /> <br /> Summary<br /> <br /> <br /> <br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| This brings us to the end of this tutorial. Let us summarize. <br /> <br /> <br /> In this tutorial, we have learnt to,<br /> <br /> * Calculate the '''norm''' of a '''matrix''' using the function '''norm()'''<br /> * Calculate '''SVD''' of a '''matrix''' using the '''function''' '''svd()'''<br /> <br /> <br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Show Slide<br /> <br /> Self assessment questions slide<br /> <br /> <br /> <br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Here is a self assessment question for you to solve<br /> <br /> 1. '''norm''''' inside brackets '''''A '''''comma '''''ord''''' is equal to inside single quotes '''''fro''' is the same as '''norm '''''inside brackets '''''A'''<br /> <br /> True or False<br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Show Slide<br /> <br /> Solution of self assessment questions on slide<br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| And the answer is True since the '''order '''''is equal to inside single quotes '''''fro''' stands for '''Frobenius norm.''' <br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Show Slide Forum<br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Please post your timed queries in this forum.<br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Show Slide Fossee Forum<br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Please post your general queries on Python in this forum.<br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Slide TBC<br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| FOSSEE team coordinates the TBC project.<br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Show Slide<br /> <br /> Acknowledgment<br /> <br /> http://spoken-tutorial.org<br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Spoken Tutorial Project is funded by NMEICT, MHRD, Govt. of India.<br /> <br /> For more details, visit this website.<br /> <br /> |-<br /> | style=&quot;background-color:#ffffff;border-top:0.5pt solid #000001;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:none;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| Previous slide<br /> | style=&quot;background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;&quot;| This is Priya from IIT Bombay signing off.<br /> <br /> Thanks for watching.<br /> <br /> |}</div>

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