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

Time	Narration
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.
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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.

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