[SciPy-Dev] matrix_sqrt for singular symmetric square matrices

[Ilhan Polat]

This is covered by LDLt decomposition with an extra step of taking the
square root of each block in D. The economy mode of this would be removing
rows/cols 0 blocks from D and L. For the second case I think a polar
decomposition would be a better approach.

Calling these factors a square root might take you out of the common
terminology though

On Sun, Oct 28, 2018 at 9:00 AM Gael Varoquaux <
gael.varoquaux at normalesup.org> wrote:

> On Sun, Oct 28, 2018 at 08:56:37AM +0100, Gael Varoquaux wrote:
> > using '@' to denote the matrix product, and S = np.diag(s) is the
> > diagonal matrix of eigenvalues. The matrix square root is then given by:
>
> >    sqrt(M) = U' @ np.diag(np.sqrt(s)) @ U
>
> I forgot to say: this is the definition used by Joseph, in his original
> post (so basically, I am backing his choice), with the only difference
> that I would not use an SVD, but and "eigh", which should be faster and
> more stable for SPD matrices (and non SPD matrices do not have a square
> root).
>
> G
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