PoojaMoolya: Created page with "{| border=1 | '''Time ''' | '''Narration''' |- | 00:01 | Welcome to the spoken tutorial on '''Basic Matrix Operations'''. |- | 00:07 | I..."

2019-05-31T12:58:33Z

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

|-
| 00:01
| Welcome to the spoken tutorial on '''Basic Matrix Operations'''.

|-
| 00:07
| In this tutorial, you will learn to, Create '''matrices''' from '''lists'''

|-
| 00:13
| Perform basic '''matrix operations''' like

addition

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| 00:19
| subtraction and multiplication

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| 00:23
| Perform '''operations''' to find out

'''determinant''' of a '''matrix'''

|-
| 00:29
| '''inverse''' of a '''matrix'''

'''Eigen values''' and '''Eigen vectors''' of a '''matrix '''

|-
| 00:37
| To record this tutorial, I am using

'''Ubuntu Linux 16.04''' operating system

|-
| 00:44
| '''Python 3.4.3''' and '''IPython 5.1.0'''

|-
| 00:51
| To practise this tutorial, you should have basic knowledge about

|-
| 00:56
| '''Lists'''

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| 00:58
| '''Arrays '''and '''accessing parts of arrays ''' and

Theoretical knowledge of '''matrix operations'''

|-
| 01:06
| If not, see the relevant '''Python''' tutorials on this website.

|-
| 01:11
| In '''Python''', we create a '''matrix''' using '''numpy matrix class.'''

|-
| 01:16
| '''Matrix operations''' can be done using '''numpy operators''' and '''functions'''.

|-
| 01:22
| Let us start '''ipython'''.

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| 01:25
| Open the '''terminal'''.

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| 01:27
| Type '''ipython3 '''and press '''Enter'''.

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| 01:31
|
From here onwards, remember to press the '''Enter''' key after typing every '''command''' on the '''terminal'''.

|-
| 01:38
| Let us create a '''matrix m1.'''

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| 01:41
| Type '''from numpy import matrix'''

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| 01:47
| Then type, '''m1 '''''is equal to''''' matrix '''''inside brackets inside square brackets '''''1''''' comma '''''2''''' comma '''''3''''' comma '''''4'''

|-
| 01:57
| Now type '''m1'''

|-
| 02:00
| This creates a '''matrix''' with one row and four columns.

|-
| 02:05
| This can be verified by typing '''m1.shape'''

This gives the output as (1, 4)

|-
| 02:15
| A '''list''' can also be converted to a '''matrix''' as follows,

Type as shown.

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| 02:23
| You can see the '''matrix m2''' with values from '''list l1.'''

|-
| 02:29
| To convert an '''array''' to a '''matrix''', use the '''asmatrix method''' in '''numpy module'''.

|-
| 02:36
| We can use '''arange '''and '''reshape methods '''to generate an '''array'''.

|-
| 02:42
| Type as shown.

'''arange''' is a '''method''' available in''' numpy.'''

|-
| 02:49
| Here it returns an '''array''' of evenly spaced values between '''1 '''and''' 9.'''

|-
| 02:55
| '''reshape''' is used to change the shape of the '''array''' to 2 rows and 4 columns.

|-
| 03:02
| '''asmatrix '''is a '''method''' available in '''numpy '''and it interprets the input as a '''matrix'''.

|-
| 03:09
| Pause the video.

Try this exercise and then resume the video.

|-
| 03:15
| Create a two dimensional '''matrix m3 '''of '''shape''' 2 by 4 with the '''elements''' 5, 6, 7, 8, 9, 10, 11, 12.

|-
| 03:25
| Hint: Use '''arange() '''and '''reshape() methods '''and''' asmatrix() function.'''

|-
| 03:31
| Switch back to the '''terminal''' for the solution.

|-
| 03:35
| Type, '''m3 '''''is equal to''''' asmatrix '''''inside brackets '''''arange '''''inside brackets '''''5 '''''comma '''''13 '''''dot '''''reshape '''''inside brackets '''''2''''' comma '''''4'''

|-
| 03:48
| Type''' m3''' You can see the required output.

|-
| 03:54
| Next let us see some '''matrix operations'''.

Type, '''m3 '''''plus''''' m2'''

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| 04:02
| It performs '''element''' by '''element''' addition, that is '''matrix''' addition.

|-
| 04:07
| Note that both the '''matrices''' should be of the same '''shape'''.

|-
| 04:12
| Similarly, type '''m3''''' minus '''''m2'''

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| 04:17
| It performs '''matrix''' subtraction, that is '''element''' by '''element''' subtraction.

|-
| 04:24
| Note that both the '''matrices''' should be of the same '''shape'''.

|-
| 04:28
| Now we can multiply a '''scalar''' i.e a number by a '''matrix''' as shown.

|-
| 04:36
| Next we will check the size of '''m2 '''by typing,

'''m2 dot shape.'''

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| 04:43
| We get a '''tuple (2, 4).'''

'''Matrix m2''' is of the shape, two by four.

|-
| 04:49
| Let us create another '''matrix''', of the order 4 by 2.

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| 04:55
|
Type, '''m4 '''''is equal to''''' asmatrix '''''inside brackets '''''arange '''''inside brackets '''''1 '''''comma '''''9''''' dot '''''reshape '''''inside brackets '''''4''''' comma '''''2'''

|-
| 05:07
| Now to check the shape, type '''m4.shape'''

We get (4,2) as the shape of '''m4'''.

|-
| 05:16
| The multiplication '''operator ''asterisk '''''is used for '''matrix''' multiplication.

|-
| 05:22
| Type '''m2 '''''asterisk''''' m4'''

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| 05:27
| Now we get output as multiplication of '''m2''' and '''m4.'''

|-
| 05:33
| Let us now see, how to find out the '''transpose''' of a '''matrix.'''

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| 05:38
| To see the content of '''m4''', type '''print''''' inside brackets '''''m4'''

|-
| 05:46
| Now type, '''print '''''inside brackets '''''m4''''' dot capital''''' T'''

|-
| 05:53
| As you saw, '''m4''' dot''' capital T''' will give the '''transpose''' of a '''matrix.'''

|-
| 05:59
| We can get the '''determinant''' of a '''square matrix''' by using the '''function det() '''in''' numpy.linalg module'''.

|-
| 06:09
| Pause the video.

Try this exercise and then resume the video.

|-
| 06:15
| Find out the '''determinant''' of this 3 by 3 '''matrix.'''

|-
| 06:20
| Switch to the '''terminal''' for the solution.

|-
| 06:23
| Type as shown.

|-
| 06:26
| The '''determinant''' of '''m5''' can be found by issuing the '''command'''

''det '''''inside brackets '''''m5'''

|-
| 06:35
| We get '''determinant''' of '''m5''' as output.

|-
| 06:39
| We can get the '''inverse''' of a '''square matrix''' by using '''inv() function '''in''' numpy.linalg module'''.

|-
| 06:48
| Let us find the '''inverse''' of the '''matrix m5.'''

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| 06:52
| Type as shown.

Then to see the '''inverse''', type '''im5'''

|-
| 07:02
| Type '''from numpy import eye, allclose'''

|-
| 07:09
| Then type, '''allclose''''' inside brackets '''''im5 '''''asterisk''''' m5 '''''comma''''' asmatrix '''''inside brackets '''''eye '''''inside brackets '''''3'''

|-
| 07:22
| This returns '''True.'''

|-
| 07:25
| We know that multiplication of a '''matrix''' with its '''inverse''' gives the '''identity matrix'''.

|-
| 07:31
| '''Identity matrix''' is created using '''eye() function'''. It is present in the '''numpy module'''.

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| 07:40
| Here '''asmatrix '''''inside brackets '''''eye '''''inside brackets '''''3''' gives '''identity matrix''' of size 3.

|-
| 07:48
| '''allclose '''is a '''function''' that returns '''True''' if two '''arrays''' are '''element''' wise equal.

|-
| 07:55
| To know more about these, we will check the documentation.

|-
| 08:00
| Type the '''function''' name followed by a question mark in '''IPython console.'''

|-
| 08:05
| Type '''eye''''' question mark''

|-
| 08:11
| To quit the documentation, press '''q'''.

|-
| 08:15
| It is a good practice to read documentation of new '''functions''' that you come across.

|-
| 08:22
| Let us now move onto '''Eigen vectors''' and '''Eigen values.'''

|-
| 08:27
|
Given a '''square matrix A'''

'''eig '''''inside brackets''''' A '''''inside square brackets''''' 0 '''gives its '''eigenvalues'''

|-
| 08:37
| '''eig '''''inside brackets''''' A '''''inside square brackets '''''1''' gives its '''eigenvector'''

|-
| 08:43
| '''eigvals '''''inside brackets '''''A '''gives its '''eigenvalues'''

|-
| 08:49
| '''eig''' and '''eigvals functions''' are present in '''numpy.linalg module'''.

|-
| 08:58
| Let us find out the '''eigenvalues''' and '''eigenvectors''' of the '''matrix m6'''.

Type as shown.

|-
| 09:07
| Now to see the value, type,'''eig '''''inside brackets '''''m6'''

|-
| 09:14
| '''diag '''''inside brackets again inside brackets '''''1 '''''comma''''' 2 '''''comma '''''3 '''
creates a '''diagonal matrix''' with 1,2,3 as diagonal '''elements''' and '''0 '''elsewhere .

|-
| 09:26
|'''diag() function '''is present in''' numpy module.'''

|-
| 09:31
| Note that '''eig '''''inside brackets '''''m6''' returned a '''tuple''' of one '''array''' and one '''matrix'''.

|-
| 09:38
|The first '''element''' in the '''tuple''' is an '''array''' of three '''eigen values'''.

|-
| 09:43
|The second '''element''' in the '''tuple''' is a '''matrix''' of three '''eigen vectors'''.

|-
| 09:48
| To get '''eigen values '''type,'''eig''''' underscore '''''value''''' is equal to''''' eig''''' inside brackets '''''m6 '''''inside square brackets '''''0'''

|-
| 10:00
| Then type '''eig '''''underscore '''''value'''

|-
| 10:04
| As you can see '''eig '''''underscore '''''value''' contains '''eigenvalues'''.

|-
| 10:09
| To get '''eigen vectors '''type,'''eig '''''underscore '''''vector '''''is equal to''''' eig''''' inside brackets '''''m6 '''''inside square brackets '''''1'''

|-
| 10:20
| Then type '''eig '''''underscore '''''vector'''

|-
| 10:25
| '''eig '''''underscore '''''vector '''contains '''eigen vector'''.

|-
| 10:29
| The '''eigen values''' can also be computed using '''eigvals() function'''.

Type as shown.

|-
| 10:39
| Then type '''eig '''''underscore '''''value1'''

|-
| 10:44
| You can see that, '''eig '''''underscore '''''value '''and''' eig '''''underscore '''''value1 '''are same.

|-
| 10:52
| This brings us to the end of this tutorial. Let us summarize.

|-
| 10:58
| In this tutorial, we have learnt to,

Create '''matrices''' using '''arrays'''

|-
| 11:03
| Add, subtract and multiply '''matrices'''

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| 11:07
| Take '''scalar''' multiple of a '''matrix'''

|-
| 11:11
| Use the '''function det()''' to find the '''determinant''' of a '''matrix'''

|-
| 11:16
| Find out the '''inverse''' of a '''matrix''' using the '''function inv() '''

|-
| 11:21
| Find out the '''eigen vectors''' and '''eigen values''' of a '''matrix''', using the '''functions eig()''' and '''eigvals()'''

|-
| 11:30
| Here are some self assessment questions for you to solve

|-
| 11:34
| First. A and B are two '''matrix objects''' of appropriate sizes. Which one of the below is correct for '''matrix''' multiplication?

|-
| 11:45
| Second. '''eig '''''inside brackets '''''A''''' inside square brackets '''''1''' and '''eigvals '''''inside brackets '''''A''' are the same. True or False?

|-
| 11:56
| And the answers,

First. '''Matrix''' multiplication between A and B is done by, A ''asterisk'' B

|-
| 12:05
| Second. False. '''eig '''''inside brackets '''''A''''' inside square brackets '''''0''' and '''eigvals '''''inside brackets '''''A''' are same, that is both will give the '''eigen values''' of '''matrix''' A.

|-
| 12:19
| Please post your timed queries in this forum.

|-
| 12:23
| Please post your general queries on Python in this forum.

|-
|12:28
| FOSSEE team coordinates the TBC project.

|-
| 12:32
| Spoken Tutorial Project is funded by NMEICT, MHRD, Govt. of India.

For more details, visit this website.

|-
| 12:42
| This is Priya from IIT Bombay signing off.

Thanks for watching.

|}

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

PoojaMoolya: Created page with "{| border=1 | '''Time ''' | '''Narration''' |- | 00:01 | Welcome to the spoken tutorial on '''Basic Matrix Operations'''. |- | 00:07 | I..."