Joint Approximate Diagonalization of Positive Definite Hermitian Matrices

Abstract

This paper provides an iterative algorithm to jointly approximately diagonalize K Hermitian positive definite matrices ${\bf\Gamma}_1$, \dots, ${\bf\Gamma}_K$. Specifically, it calculates the matrix B which minimizes the criterion $\sum_{k=1}^K n_k [\log \det\diag(\B\C_k\B^*) - \log\det(\B\C_k\B^*)]$, nk being positive numbers, which is a measure of the deviation from diagonality of the matrices BCkB*$. The convergence of the algorithm is discussed and some numerical experiments are performed showing the good performance of the algorithm.