Eigenvalue of A^(tr) * A and A * A^(tr)

[devout anvil]

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[silver garnet]

Now, apparently this doesn't hold if lambda = 0. But couldn't I just argue exactly like in the proof above? Where exactly does it fail

[cobalt minnow]

I think the main problem (and what MSE posts allude to) is that you're assuming your w isn't 0 implicitly

The only good explanation I found for why the != 0 condition is requires is because you're proving the lambda-eigenspaces of $AA^T$ and $A^TA$ are isomorphic, and the isomorphism used invokes 1/sqrt(lambda)

[ivory ruin]

Omegabet_

[cobalt minnow]

https://math.stackexchange.com/questions/2672419/let-a-be-an-m-times-n-matrix-show-ata-and-aat-have-the-same-eigenval

last comment shows the proposed S and T are infact inverses of one another

(there's probably also some connection to the SVD of A that I'm neglecting/forgetting)

[silver garnet]

Thank you!

[hoary wadi]

@silver garnet has given 1 rep to @cobalt minnow

[silver garnet]

+close