PoojaMoolya: Created page with "{| border=1 | '''Time ''' | '''Narration''' |- | 00:01 | Welcome to the spoken tutorial on '''Advanced matrix operations'''. |- | 0..."

2019-06-11T05:19:22Z

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{| border=1
| <center>'''Time '''</center>
| <center>'''Narration'''</center>

|-
| 00:01
| Welcome to the spoken tutorial on '''Advanced matrix operations'''.

|-
| 00:07
| In this tutorial, you will learn to, find''' Frobenius''' and '''infinity norm''' of a '''matrix'''

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| 00:14
| Find '''singular value decomposition''' of a '''matrix'''.

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| 00:19
| To record this tutorial, I am using '''Ubuntu Linux 16.04''' operating system

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| 00:26
| '''Python 3.4.3 '''and '''IPython 5.1.0'''

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| 00:33
| To practise this tutorial, you should know about

'''Lists, arrays '''and accessing parts of '''arrays '''and performing basic''' matrix operations'''

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| 00:46
| If not, see the relevant '''Python''' tutorials on this website.

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| 00:51
| First we will see about '''flatten''' function.

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| 00:55
| '''flatten() function''' returns a copy of the '''array''', collapsed into one '''dimension'''.

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| 01:01
| It can be used to convert a '''multidimensional matrix''' into a '''single dimension matrix'''

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| 01:08
| Let us start '''ipython'''.

Open the '''terminal.'''

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| 01:13
| Type, '''ipython3 '''and press '''Enter'''.

From here onwards, remember to press the '''Enter''' key after typing every '''command''' on the '''terminal'''.

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| 01:25
| Now let us see how to create '''arrays'''

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| 01:29
| Type '''from numpy import asmatrix comma arange'''

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| 01:35
| '''a''''' is equal to''''' asmatrix '''''inside brackets''''' arange '''''inside brackets '''''1''''' comma '''''10''''' dot '''''reshape '''''inside brackets '''''3 '''''comma '''''3'''

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| 01:48
| Then type, '''a'''

Now type, '''a''''' dot '''''flatten''''' open and close brackets''

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| 01:57
| First we imported''' arange function''' from '''numpy module'''.

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| 02:02
| Here, we can see '''3 by 3 matrix''' is converted into one '''dimensional matrix'''.

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| 02:08
| Next we will see about '''frobenius norm.'''

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| 02:12
|It is defined as the '''square root''' of the sum of the '''absolute squares''' of its '''elements'''.

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| 02:18
| Pause the video.

Try this exercise and then resume the video.

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| 02:24
| Find out the '''frobenius norm''' of the '''inverse''' of the given '''4 by 4 matrix'''.

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| 02:30
| Switch back to the '''terminal''' for the solution.

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| 02:34
| Type

'''m '''''is equal to''''' asmatrix '''''inside brackets''''' arange '''''inside brackets '''''1''''' comma '''''17 '''''dot '''''reshape '''''inside brackets '''''4''''' comma '''''4'''

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| 02:46
| Here, we have used '''asmatrix, arange''' and '''reshape functions'''.

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| 02:52
|We created a '''matrix''' of size '''4 by 4''' containing '''elements''' from 1 to 16.

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| 02:59
| Now type,

'''m '''''inside square brackets '''''0 '''''comma '''''1''''' is equal to''''' 0'''

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| 03:06
|'''m '''''inside square brackets '''''1''''' comma '''''3 '''''is equal to''''' 0'''

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| 03:12
| Then type, '''m'''

We changed the value of '''element''' at row 0 column 1 and row 1 column 3 to 0.

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| 03:23
| In order to find out the '''Frobenius norm''' of the '''inverse''' of '''matrix m''', type as shown.

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| 03:33
| '''norm function''' is available in''' numpy.linalg module.'''

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| 03:39
| Next, we will see about '''infinity norm''' of a '''matrix.'''

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| 03:44
|It is defined as the maximum value of sum of the '''absolute value''' of '''elements''' in each row.

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| 03:51
| Pause the video.

Try this exercise and then resume the video.

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| 03:57
| Find the '''infinity norm''' of the '''matrix im.'''

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| 04:01
| Switch back to the '''terminal''' for the solution.

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| 04:05
| To find out the '''Infinity norm''' of the '''matrix im''', type as shown.

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| 04:11
|Here value for '''ord parameter''' is passed as '''inf''' to calculate '''infinity norm'''.

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| 04:18
| To know more about '''norms''' type '''norm '''''question mark''

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| 04:24
| Press '''q''' to exit.

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| 04:28
| Next we will see about '''singular value decomposition.'''

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| 04:33
|In '''linear algebra''', the '''singular value decomposition''' is factorization of '''real''' or '''complex matrix.'''

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| 04:42
| The '''SVD''' of '''matrix m1''' can be found using '''svd function''' available in the '''numpy.linalg module'''.

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| 04:52
|Type as shown.

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| 04:56
|'''svd''' returns a '''tuple''' of 3 '''elements'''.

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| 05:00
| We have unpacked these values into '''variable U, sigma''' and '''V''''' underscore '''''conjugate.'''

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| 05:08
| Type, Capital '''U'''

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| 05:12
| Type,''' sigma'''

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| 05:15
| Type, Capital '''V''''' underscore '''''conjugate'''

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| 05:20
| We can validate the '''singular value decomposition''' by comparing the product of:

'''U, sigma''' and '''V '''''underscore '''''conjugate '''with''' m1'''

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| 05:30
|'''sigma''' is a one '''dimensional array''' which contains only the '''diagonal elements''' of the '''matrix'''.

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| 05:37
| Type as shown.

We first convert this '''array''' to a '''matrix'''.

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| 05:43
| Type '''smat'''

'''smat''' is a 2 by 3 '''zero matrix'''

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| 05:51
| Now type, '''smat''''' inside square brackets colon '''''2 '''''comma''''' '''''colon '''''2 '''''is equal to''''' diag '''''inside brackets '''''sigma'''

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| 06:02
| Then type '''smat'''

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| 06:06
| This replaces values at row 0 column 0 and row 1 column 1 in '''smat '''with values from '''sigma. '''

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| 06:16
| '''smat''' is a '''2 by 3 matrix''' created for multiplications by placing values of sigma as '''diagonal elements''' and zero elsewhere.

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| 06:27
| Type as shown.

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| 06:33
| It returns '''True'''.

It means '''elements''' in '''m1''' and in product of''' U, sigma '''and''' V''''' underscore '''''conjugate '''are equal.

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| 06:43
| This brings us to the end of this tutorial. Let us summarize.

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| 06:49
| In this tutorial, we have learnt to, Calculate the '''norm''' of a '''matrix''' using the '''function norm()'''

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| 06:56
| Calculate '''SVD''' of a '''matrix''' using the '''function svd()'''

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| 07:01
| Here is a self assessment question for you to solve

'''norm''''' inside brackets '''''A '''''comma '''''ord''''' is equal to inside single quotes '''''fro''' is same as '''norm '''''inside brackets '''''A'''

True or False.

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| 07:19
| And the answer is True, since the '''order '''''is equal to inside single quotes '''''fro''' stands for '''Frobenius norm.'''

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| 07:29
| Please post your timed queries in this forum.

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| 07:33
| Please post your general queries on Python in this forum.

|-
| 07:37
| FOSSEE team coordinates the TBC project.

|-
| 07:41
| Spoken Tutorial Project is funded by NMEICT, MHRD, Govt. of India.

For more details, visit this website.

|-
| 07:50
| This is Priya from IIT Bombay signing off.

Thanks for watching.

|}

Python-3.4.3/C3/Advanced-Matrix-Operations/English-timed - Revision history

PoojaMoolya: Created page with "{| border=1 | '''Time ''' | '''Narration''' |- | 00:01 | Welcome to the spoken tutorial on '''Advanced matrix operations'''. |- | 0..."