Re: [Numpy-discussion] Matrix square root

[Konrad H. <hi...@cn...>]

On Thursday 04 September 2003 16:42, Andrew Nesbit wrote:
> I need a function equivalent to Matlab's sqrtm, i.e., a square root
> for matrices.
>
> I constructed the following definition:
>
> def sqrtm(M):
>     (U,S,VT) =3D LinearAlgebra.singular_value_decomposition(M)
>     D =3D MLab.diag(sqrt(S))
>     return matrixmultiply(matrixmultiply(U,D),VT)
>
> but this technique only works for Hermitian, positive definite
> matrices.  The matrices I operate on don't necessarily satisfy that
> condition.

I'd use an eigenvalue decomposition, then take the square root of the=20
eigenvalues, and then apply the diagonlization matrix in reverse. If you=20
convert to eigenvalues to complex before taking the square root, this wil=
l=20
work for non-positive-definite matrices, yielding a complex result.

Konrad.
--=20
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