Python-3.4.3/C3/Basic-Matrix-Operations/English-timed
From Script | Spoken-Tutorial
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| 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 |
| 00:19 | subtraction and multiplication |
| 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 |
| 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. |
| 01:25 | Open the terminal. |
| 01:27 | Type ipython3 and press Enter. |
| 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. |
| 01:41 | Type from numpy import matrix |
| 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. |
| 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 |
| 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 |
| 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. |
| 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. |
| 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 |
| 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. |
| 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. |
| 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. |
| 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 |
| 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. |
