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

Time	Narration
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
00:14	Find singular value decomposition of a matrix.
00:19	To record this tutorial, I am using Ubuntu Linux 16.04 operating system
00:26	Python 3.4.3 and IPython 5.1.0
00:33	To practise this tutorial, you should know about Lists, arrays and accessing parts of arrays and performing basic matrix operations
00:46	If not, see the relevant Python tutorials on this website.
00:51	First we will see about flatten function.
00:55	flatten() function returns a copy of the array, collapsed into one dimension.
01:01	It can be used to convert a multidimensional matrix into a single dimension matrix
01:08	Let us start ipython. Open the terminal.
01:13	Type, ipython3 and press Enter. From here onwards, remember to press the Enter key after typing every command on the terminal.
01:25	Now let us see how to create arrays
01:29	Type from numpy import asmatrix comma arange
01:35	a is equal to asmatrix inside brackets arange inside brackets 1 comma 10 dot reshape inside brackets 3 comma 3
01:48	Then type, a Now type, a dot flatten open and close brackets
01:57	First we imported arange function from numpy module.
02:02	Here, we can see 3 by 3 matrix is converted into one dimensional matrix.
02:08	Next we will see about frobenius norm.
02:12	It is defined as the square root of the sum of the absolute squares of its elements.
02:18	Pause the video. Try this exercise and then resume the video.
02:24	Find out the frobenius norm of the inverse of the given 4 by 4 matrix.
02:30	Switch back to the terminal for the solution.
02:34	Type m is equal to asmatrix inside brackets arange inside brackets 1 comma 17 dot reshape inside brackets 4 comma 4
02:46	Here, we have used asmatrix, arange and reshape functions.
02:52	We created a matrix of size 4 by 4 containing elements from 1 to 16.
02:59	Now type, m inside square brackets 0 comma 1 is equal to 0
03:06	m inside square brackets 1 comma 3 is equal to 0
03:12	Then type, m We changed the value of element at row 0 column 1 and row 1 column 3 to 0.
03:23	In order to find out the Frobenius norm of the inverse of matrix m, type as shown.
03:33	norm function is available in numpy.linalg module.
03:39	Next, we will see about infinity norm of a matrix.
03:44	It is defined as the maximum value of sum of the absolute value of elements in each row.
03:51	Pause the video. Try this exercise and then resume the video.
03:57	Find the infinity norm of the matrix im.
04:01	Switch back to the terminal for the solution.
04:05	To find out the Infinity norm of the matrix im, type as shown.
04:11	Here value for ord parameter is passed as inf to calculate infinity norm.
04:18	To know more about norms type norm question mark
04:24	Press q to exit.
04:28	Next we will see about singular value decomposition.
04:33	In linear algebra, the singular value decomposition is factorization of real or complex matrix.
04:42	The SVD of matrix m1 can be found using svd function available in the numpy.linalg module.
04:52	Type as shown.
04:56	svd returns a tuple of 3 elements.
05:00	We have unpacked these values into variable U, sigma and V underscore conjugate.
05:08	Type, Capital U
05:12	Type, sigma
05:15	Type, Capital V underscore conjugate
05:20	We can validate the singular value decomposition by comparing the product of: U, sigma and V underscore conjugate with m1
05:30	sigma is a one dimensional array which contains only the diagonal elements of the matrix.
05:37	Type as shown. We first convert this array to a matrix.
05:43	Type smat smat is a 2 by 3 zero matrix
05:51	Now type, smat inside square brackets colon 2 comma colon 2 is equal to diag inside brackets sigma
06:02	Then type smat
06:06	This replaces values at row 0 column 0 and row 1 column 1 in smat with values from sigma.
06:16	smat is a 2 by 3 matrix created for multiplications by placing values of sigma as diagonal elements and zero elsewhere.
06:27	Type as shown.
06:33	It returns True. It means elements in m1 and in product of U, sigma and V underscore conjugate are equal.
06:43	This brings us to the end of this tutorial. Let us summarize.
06:49	In this tutorial, we have learnt to, Calculate the norm of a matrix using the function norm()
06:56	Calculate SVD of a matrix using the function svd()
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.
07:19	And the answer is True, since the order is equal to inside single quotes fro stands for Frobenius norm.
07:29	Please post your timed queries in this forum.
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.

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