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A comment on Why is it important for a matrix to be square? (2018). Parent comment

Re:Why is it important for a matrix to be square? (2018) by mgraczyk on Sunday June 21, 2020 @01:37PM (#23593627)
Singular values of a transform are defined using the "operator norm" of the transform.

The norm is defined in terms of the inner product.

On the other hand, eigenvalues are defined with using only the transform and scalar multiplication, which does not require an inner product.

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Re:Why is it important for a matrix to be square? (2018) by tsbinz on Sunday June 21, 2020 @01:50PM (#23593747)
I'm not sure you need to do that (define singular values via the operator norm), but one thing I don't see a solution for is getting rid of the requirement of the inner product for the definition of the adjoint.
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