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) = LinearAlgebra.singular_value_decomposition(M) D = 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 eigenvalues, and then apply the diagonlization matrix in reverse. If you convert to eigenvalues to complex before taking the square root, this will work for non-positive-definite matrices, yielding a complex result. Konrad. -- ------------------------------------------------------------------------------- Konrad Hinsen | E-Mail: hinsen@cnrs-orleans.fr Centre de Biophysique Moleculaire (CNRS) | Tel.: +33-2.38.25.56.24 Rue Charles Sadron | Fax: +33-2.38.63.15.17 45071 Orleans Cedex 2 | Deutsch/Esperanto/English/ France | Nederlands/Francais -------------------------------------------------------------------------------