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My statistics research requires me to understand the non-uniqueness of SVD in the degenerate case of repeated singular values. I believe that the statements and proofs on this StackExchange posts are ...

In order to solve a boundary problem for a conducting hemisphere, the following matrix equation arises (derived from the boundary condition on the curved part of the surface) where we must solve for ...

Let's consider the usual Hilbert transform $H$ defined as $$Hf = P.V. (\frac{1}{x}*f).$$ A well-known unique continuation principle states that if $Hf = f =0$ on some interval $I$, then $f \equiv 0$. ...