Joint Approximate Diagonalization of Positive Definite Hermitian Matrices

This paper provides an iterative algorithm to jointly approximately diagonalize K Hermitian positive definite matrices Γ₁, , ΓK. Specifically, it calculates the matrix B which minimizes the criterion ∑ₖ₌₁K nₖ [log (ₖ^*) - log(ₖ^*)], n k being positive numbers, which is a measure of the deviation from diagonality of the matrices BC k B*$. The convergence of the algorithm is discussed and some numerical experiments are performed showing the good performance of the algorithm.