Priyacst at 13:26, 27 November 2018

2018-11-27T13:26:21Z

Priyacst: Created page with "'''Title of script''': '''Basic Matrix Operations''' '''Author: Puneeth, Thirumalesh H S, Arun KP''' '''Keywords: Python, IPython, matrices, determinant, reshape, arange, ei..."

2018-11-01T08:30:12Z

Created page with "'''Title of script''': '''Basic Matrix Operations''' '''Author: Puneeth, Thirumalesh H S, Arun KP''' '''Keywords: Python, IPython, matrices, determinant, reshape, arange, ei..."

New page

'''Title of script''': '''Basic Matrix Operations'''

'''Author: Puneeth, Thirumalesh H S, Arun KP'''

'''Keywords: Python, IPython, matrices, determinant, reshape, arange, eigen values, eigen vectors, transpose of matrix'''

{| style="border-spacing:0;"
| style="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;"| <center>'''Visual Cue '''</center>
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| <center>'''Narration'''</center>

|-
| style="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;"| Show Slide title
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Welcome to the spoken tutorial on '''Basic Matrix Operations'''.

|-
| style="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;"| Show Slide

Objectives

| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| In this tutorial, you will learn to,

* Create '''matrices''' from lists
* Perform basic '''matrix''' operations like
** addition
** subtraction and
** multiplication
* Perform operations to find out

* '''determinant''' of a '''matrix'''
* '''inverse''' of a '''matrix'''
* '''eigenvalues''' and '''eigenvectors''' of a '''matrix '''

|-
| style="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;"| Show Slide

System Specifications
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| To record this tutorial, I am using

* '''Ubuntu Linux 16.04''' operating system
* '''Python 3.4.3'''
* '''IPython 5.1.0'''

|-
| style="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;"| Show Slide

Pre-requisites

| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| To practise this tutorial, you should have basic knowledge about

* '''Lists'''
* '''arrays '''and '''accessing parts of arrays '''and
* theoretical knowledge of '''matrix operations'''

If not, see the relevant '''Python''' tutorials on this website.

|-
| style="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;"| Slide:
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| * In python, we create a matrix using '''numpy matrix class.'''
* Matrix operations can be done using '''numpy''' operators and functions.

|-
| style="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;"| Type,

'''ipython3 '''
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Let us start '''ipython'''.

Open the '''terminal'''.

|-
| style="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;"| Type '''ipython3'''

Press''' Enter'''
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Type '''ipython3 '''and press Enter.

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

|-
| style="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;"| Type,

'''from numpy import matrix'''

'''m1 = matrix<nowiki>([1,2,3,4])</nowiki>'''

'''m1'''

Point to the output
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Let us create a matrix''' m1.'''

Type,

'''from numpy import matrix'''

Then type,

'''m1 '''''is equal to''''' matrix '''''inside brackets inside square brackets '''''1''''' comma '''''2''''' comma '''''3''''' comma '''''4'''

Now type,

'''m1'''

This creates a matrix with one row and four columns.

|-
| style="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;"| Type,

'''m1.shape'''

Highlight the output
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| This can be verified by typing

'''m1.shape'''

This gives the output as (1, 4)

|-
| style="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;"| Type,

'''<nowiki>l1 = [[1,2,3,4],[5,6,7,8]]</nowiki>'''

'''m2 = matrix(l1)'''

'''print(m2)'''

Highlight the output
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| A list can also be converted to a '''matrix''' as follows,

Type as shown.

You can see the matrix '''m2''' with values from list '''l1.'''

|-
| style="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;"| Slide:'''asmatrix'''
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| * To convert an array to a matrix, use the '''asmatrix''' method in '''numpy '''module.
* We can use '''arange '''and '''reshape methods '''to generate an array.

|-
| style="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;"| Highlight according to narration

Type,

'''from numpy import asmatrix,arange'''

'''m2_array = asmatrix(arange(1,9).reshape(2,4))'''

'''m2_array'''
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Type as shown.

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

Here it returns an array of evenly spaced values between '''1 '''and''' 8.'''

'''reshape''' is used to change the shape of the array to 2 rows and 4 columns.

'''asmatrix '''is a method available in '''numpy '''and it''' '''interprets the input as a matrix.

|-
| style="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;"|
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Pause the video.

Try this exercise and then resume the video.

|-
| style="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;"| Show Slide

Assignment 1
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Create a two dimensional '''matrix''' '''m3 '''of '''shape''' 2 by 4 with the elements 5, 6, 7, 8, 9, 10, 11, 12.

Hint: Use '''arange() '''and '''reshape() methods '''and''' asmatrix() function.'''

|-
| style="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;"| Switch to the terminal
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Switch back to the terminal for the solution.

|-
| style="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;"| Type,

'''m3 = asmatrix(arange(5,13).reshape(2,4))'''

Type,''' m3'''
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Type,

'''m3 '''''is equal to''''' asmatrix '''''inside brackets '''''arange '''''inside brackets '''''5 '''''comma '''''13 '''''dot '''''reshape '''''inside brackets '''''2''''' comma '''''4'''

Type,''' m3'''

You can see the required output.

|-
| style="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;"| Type,

'''m3 + m2'''
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Next let us see some '''matrix''' operations.

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

It performs element by element addition, that is '''matrix''' addition.

Note that both the '''matrices''' should be of the same '''shape'''.

|-
| style="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;"| Type,

'''m3 - m2'''
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Similarly, type '''m3''''' minus '''''m2'''

It performs '''matrix''' subtraction, that is element by element subtraction.

Note that both the '''matrices''' should be of the same '''shape'''.

|-
| style="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;"| Type,

'''6.5 * m2'''
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Now we can multiply a scalar i.e a number by a matrix as shown.

|-
| style="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;"| Type,

'''m2.shape'''
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Next we will check the size of '''m2 '''by typing,

'''m2.shape.'''

We get a '''tuple''' '''(2, 4).'''

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

|-
| style="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;"| Type,

'''m4 = asmatrix(arange(1,9).reshape(4,2))'''
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Let us create another '''matrix''', of the order 4 by 2.

Type,

'''m4 '''''is equal to''''' asmatrix '''''inside brackets '''''arange '''''inside brackets '''''1 '''''comma '''''9''''' dot '''''reshape '''''inside brackets '''''4''''' comma '''''2'''

|-
| style="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;"| Type

'''m4.shape'''
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Now to check the shape, type,

'''m4.shape'''

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

|-
| style="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;"| Type,

'''m2 * m4'''

Highlight the output
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| The''' multiplication operator''' ''asterisk ''is used for '''matrix''' multiplication.

Type,

'''m2 '''''asterisk''''' m4'''

Now we get output as multiplication of '''m2''' and '''m4.'''

|-
| style="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;"| Type,

'''print (m4)'''

| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Let us now see, how to find out the '''transpose''' of a '''matrix.'''

To see the content of m4, type

'''print''''' inside brackets '''''m4'''

|-
| style="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;"| Type,

'''print(m4.T)'''

Point to the output
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Now type,

'''print '''''inside brackets '''''m4''''' dot capital''''' T'''

As you saw, '''m4''' dot''' capital T''' will give the transpose of a '''matrix.'''

|-
| style="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;"| Show Slide:Determinant of a matrix
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| The '''determinant''' of a square '''matrix''' is obtained by using the function '''det() '''in''' numpy.linalg''' module.

|-
| style="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;"|
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Pause the video.

Try this exercise and resume the video.

|-
| style="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;"| Show Slide: Exercise
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Find out the '''determinant''' of this 3 by 3 '''matrix.'''

|-
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.088cm;padding-right:0.191cm;"| Switch to the terminal for solution.
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.088cm;padding-right:0.191cm;"| Switch to the terminal for the solution.

|-
| style="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;"| Type,

'''from numpy.linalg import det'''

'''<nowiki>m5 = matrix([[2,-3,1],[2,0,-1],[1,4,5]])</nowiki>'''

'''det(m5)'''
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Type as shown.

The '''determinant''' of '''m5''' can be found by issuing the '''command,'''

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

We get determinant of '''m5''' as output.

|-
| style="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;"| Show Slide

'''Inverse''' of a '''matrix'''
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| The '''inverse''' of a square '''matrix''' can be obtained using '''inv() function '''in''' numpy.linalg '''module.

|-
| style="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;"| Type,

'''from numpy.linalg import inv'''

'''im5 = inv(m5)'''

Type,

'''im5'''
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Let us find the '''inverse''' of the '''matrix m5.'''

Type as shown.

Then to see the the inverse, type

'''im5'''

|-
| style="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;"| Type,

'''from numpy import eye,allclose'''

'''allclose(im5 * m5, asmatrix(eye(3)))'''

Highlight '''eye'''

Highlight '''asmatrix(eye(3)))'''

Highlight '''allclose'''

Type,

'''eye?'''
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Type,

'''from numpy import eye,allclose'''

Then type,

'''allclose''''' inside brackets '''''im5 '''''asterisk''''' m5 '''''comma''''' asmatrix '''''inside brackets '''''eye '''''inside brackets '''''3'''

This returns '''True.'''

We know that multiplication of a matrix with its inverse gives the '''identity matrix'''.

'''Identity matrix''' is created using '''eye()''' function. It is present in the '''numpy''' module.

Here '''asmatrix '''''inside brackets '''''eye '''''inside brackets '''''3''' gives identity matrix of size 3'''.'''

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

To know more about these, we will check the documentation.

Type the function name followed by a question mark in IPython console.

Type,

'''eye''''' question mark''

To quit the documentation, press '''q'''.

It is a good practice to read documentation of new functions that you come across.

|-
| style="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;"| Show Slide

'''eigenvectors''' and '''eigenvalues'''

| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Let us now move onto '''eigenvectors''' and '''eigenvalues'''

Given a '''square matrix A'''

* '''eig '''''inside brackets''''' A '''''inside square brackets''''' 0 '''gives its '''eigenvalues'''
* '''eig '''''inside brackets''''' A '''''inside square brackets '''''1''' gives its '''eigenvector'''
* '''eigvals '''''inside brackets '''''A '''gives its '''eigenvalues'''

'''eig''' and '''eigvals''' functions are present in '''numpy.linalg''' module.

|-
| style="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;"| Type,

'''from numpy import diag'''

'''from numpy.linalg import eig'''

'''m6=asmatrix(diag((1, 2, 3)))'''

Type,

'''eig(m6)'''

Highlight '''diag((1, 2, 3)))'''

Highlight

'''<nowiki>(array([1., 2., 3.]), matrix([[1., 0., 0.],</nowiki>'''

'''<nowiki>[0., 1., 0.],</nowiki>'''

'''<nowiki>[0., 0., 1.]]))</nowiki>'''

Put box to array

Put box to matrix
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Let us find out the '''eigenvalues''' and '''eigenvectors''' of the '''matrix''' '''m6'''.

Type as shown.

Now to see the value, type,'''eig '''''inside brackets '''''m6'''

'''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 .

'''diag() function '''is present in''' numpy '''module

Note that '''eig '''''inside brackets '''''m6''' returned a tuple of one array and one matrix.

The first element in the tuple is an array of three eigenvalues.

The second element in the tuple is a matrix of three eigenvectors.

|-
| style="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;"| Type,

'''<nowiki>eig_value = eig(m6)[0]</nowiki>'''

'''eig_value'''
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| To get '''eigenvalues '''type,'''eig''''' underscore '''''value''''' is equal to''''' eig''''' inside brackets '''''m6 '''''inside square brackets '''''0'''

Then type,

'''eig '''''underscore '''''value'''

As you can see '''eig '''''underscore '''''value''' contains '''eigenvalues'''.

|-
| style="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;"| Type,

'''<nowiki>eig_vector = eig(m6)[1]</nowiki>'''

'''eig_vector'''
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| To get '''eigenvectors '''type,'''eig '''''underscore '''''vector '''''is equal to''''' eig''''' inside brackets '''''m6 '''''inside square brackets '''''1'''

Then type,

'''eig '''''underscore '''''vector'''

'''eig '''''underscore '''''vector '''contains eigenvector.

|-
| style="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;"| Type,

'''from numpy.linalg import eigvals'''

'''eig_value1 = eigvals(m6)'''

Then type,

'''eig_value1'''

Show both the outputs
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| The '''eigenvalues''' can also be computed using '''eigvals() '''function.

Type as shown.

Then type,

'''eig '''''underscore '''''value1'''

You can see that, '''eig '''''underscore '''''value '''and''' eig '''''underscore '''''value1 '''are same.

|-
| style="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;"| Show Slide

Summary

| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| This brings us to the end of this tutorial. Let us summarize.

In this tutorial, we have learnt to,

* Create '''matrices''' using '''arrays'''
* Add, subtract and multiply matrices
* Take scalar multiple of a matrix
* Use the '''function''' '''det()''' to find the '''determinant''' of a '''matrix'''
* Find out the '''inverse''' of a '''matrix''',using the function '''inv() '''
* Find out the '''eigenvectors''' and '''eigenvalues''' of a '''matrix''', using the functions '''eig()''' and '''eigvals()'''

|-
| style="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;"| Show Slide

Self assessment questions

| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Here are some self assessment questions for you to solve

# A and B are two matrix objects of appropriate sizes. Which one of the below is correct for Matrix multiplication?
# '''eig '''''inside brackets '''''A''''' inside square brackets '''''1''' and '''eigvals '''''inside brackets '''''A''' are the same. True or False

|-
| style="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;"| Show Slide 13

Solution of self assessment questions

| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| And the answers,

# Matrix multiplication between A and B is done by, A ''asterisk'' B
# False. '''eig '''''inside brackets '''''A''''' inside square brackets '''''0''' and '''eigvals '''''inside brackets '''''A''' are same, that is both will give the '''eigenvalues''' of '''matrix''' A.

|-
| style="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;"| Show Slide Forum
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Please post your timed queries in this forum.

|-
| style="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;"| Show Slide Fossee Forum
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Please post your general queries on Python in this forum.

|-
| style="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;"| Show slide TBC
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| FOSSEE team coordinates the TBC project.

|-
| style="background-color:#ffffff;border-top:none;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;"| Show Slide

Acknowledgment

http://spoken-tutorial.org
| style="background-color:#ffffff;border-top:none;border-bottom:0.5pt solid #000001;border-left:0.5pt solid #000001;border-right:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| Spoken Tutorial Project is funded by NMEICT, MHRD, Govt. of India.

For more details, visit this website.

|-
| style="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;"| Previous slide
| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| This is Priya from IIT Bombay signing off.

Thanks for watching.

|}

@@ Line 318: / Line 318: @@
 |-
 | style="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;"| Show Slide:Determinant of a matrix
-| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| The '''determinant''' of a '''square matrix''' is obtained by using the '''function det() '''in''' numpy.linalg module'''.
+| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| We can get the  '''determinant''' of a '''square matrix''' by using the '''function det() '''in''' numpy.linalg module'''.
 |-
@@ Line 357: / Line 357: @@
 '''Inverse''' of a '''matrix'''
-| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| The '''inverse''' of a '''square matrix''' can be obtained using '''inv() function '''in''' numpy.linalg module'''.
+| style="background-color:#ffffff;border:0.5pt solid #000001;padding-top:0cm;padding-bottom:0cm;padding-left:0.095cm;padding-right:0.191cm;"| We can get the  '''inverse''' of a '''square matrix''' by using '''inv() function '''in''' numpy.linalg module'''.
 |-
@@ Line 494: / Line 494: @@
-'''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 .
+'''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 .

← Older revision		Revision as of 05:19, 8 November 2018
Line 177:		Line 177:


−	Here it returns an array of evenly spaced values between '''1 '''and''' 8.'''	+	Here it returns an array of evenly spaced values between '''1 '''and''' 9.'''

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

Nancyvarkey at 12:56, 7 December 2018

Priyacst at 13:26, 27 November 2018

Nancyvarkey at 14:55, 18 November 2018

Priyacst at 05:19, 8 November 2018

Priyacst: Created page with "'''Title of script''': '''Basic Matrix Operations''' '''Author: Puneeth, Thirumalesh H S, Arun KP''' '''Keywords: Python, IPython, matrices, determinant, reshape, arange, ei..."