Simultaneous diagonalization of skew-symmetric matrices in the symplectic group

Abstract

Many source separation algorithms rely on the approximate simultaneous diagonalization of matrices. While there exist very efficient algorithms for symmetric matrices, the skew-symmetric case turned out to be more difficult. Here we show how the often used whitening/rotation approach for symmetric matrices can be translated to this case. While the former leads to orthogonal transformations in Euclidean space, the latter leads to symplectic transformations in symplectic space. It is demonstrated that the resulting algorithm is more stable than a naïve diagonalization that does not respect the symplectic structure of the problem. © 2012 Springer-Verlag.