Linear Algebra - Lecture 42 - The Singular Value Decomposition

In this lecture, we discuss the singular value decomposition, which can be used to decompose any matrix.

[cabadger]

just went through the whole seires for review, What a gold mine!

[cooking]

I've been using Python for SVD but I think Mathematica is a lot nicer since it leaves the answer with square roots.

[Unstable_Diffusion]

@12:12 don't you mean that the matrix V's columns are a basis of R^n, not R^m?

[chenlecong]

11:37 Emm.... I really don't get the part where you extend the basis. I thought the matrix B that you form still comprises of vectors from U1 to Ur.Then even if you solve B^T X=0 to get a basis, that basis should still comprise of vectors from U1 to Ur and not U1 to Um?Sorry though if it sounds stupid…