Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points

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MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018
Instructor: Gilbert Strang

In this lecture, Professor Strang reviews counting the free parameters in a variety of key matrices. He then moves on to finding saddle points from constraints and Lagrange multipliers.

License: Creative Commons BY-NC-SA

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Dear Professor Strang, you and your lectures are more than gold. I just googled what the rarest and most precious metal is, and it turns out to be Palladium, so you and your lectures are pure Palladium!
Everything in the video is clearly explained, informative, clarifying and vastly illuminating. I'm excited about what is to come in next in the video lectures!
Bravo and applause

elyepes

DR. Strang thank you for counting and verifying the Parameters in SVD, LU, QR and Saddle Points in numerical linear algebra.

georgesadler

I love watching Prof Strang suddenly have an epiphany. It's like he wants to jump up and shout "Eureka!"

financeexplainedgraphics

@26:46: mr + nr - r^2 = mn - (m-r)(n-r) makes sense as all (mn) parameters of A less a redundant bit due to the low rank.

carl

Anybody found that there are no Ads in MIT OCW, wow!

allandogreat

Around 41:33, I think the number of pivots should be (n pos + m neg) pivots since A is a m by n matrix and (-A*inv(S)*A^T) is a m by m matrix.

RC.

@29:30, why does d/dx( L' (A x) ) become A' L? ( ' = transpose, L = lambda, d/dx = partial der.)

rogiervdw

Where can we get the notes of the class which are referred in the lecture so many times?

saketdwivedi

at 40:00, is the block elimination right? I guess [ I 0 : -A*inv(S) I]

kirinkirin

At 39:55, the professor multiply [A S-1] to the left side of [S AT; A 0] to get [S AT; 0 -A*S-1*AT]. Can anybody please explain the purpose of this calculation ? Thanks in advance!

shenzheng

at [46:30], he first said that the derivative of Rayleigh's quotient at the saddle points are zero, and it sounds like to me that he was recorrecting it by the eigenvectors, and how the values of the R(x) would be the eigenvalues. Can anybody shade some light? Thanks in advance.

vaghawanojha

Who knows for sure with deminsions. You do good to dream the Riemann.

brendawilliams

13:50 - it is a kind of reverse-engineering proof...

PrzemyslawSliwinski

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