How to prove $V*V^T=I$ in SVD?

Question

How to prove $V*V^T=I$ in SVD: $M=U*S*V^T$?

It's easy to understand $V^T*V=I$. It seems $V*V^T=I$, but how to prove it?

score 0 · Accepted Answer · answered Oct 20 '14 at 17:07

0

if $A$ and $B$ are square matrix, such that $AB=I$, then $BA=I$. Because $B$, is inverse of $A$, and the inverse is a matrix is unique.

answered Oct 20 '14 at 17:07

CLAUDE

So for square matrix, there always exists $AB=I <=> BA=I$, right? – CyberPlayerOne Oct 20 '14 at 17:18
Yes. And $B$ is inverse of $A$ – CLAUDE Oct 20 '14 at 17:19

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