Institution: | aUniversity of Split, Faculty of Electrical Engineering, Mechanical Engineering, and Naval Architecture, R. Boškovića b.b, 21000 Split, Croatia bFern universität Hagen, Lehrgebiet Mathematische Physik, Postfach 940, D-58084 Hagen, Germany |
Abstract: | The hyperbolic eigenvector matrix is a matrix X which simultaneously diagonalizes the pair (H,J), where H is Hermitian positive definite and J = diag(±1) such that X*HX = Δ and X*JX = J. We prove that the spectral condition of X, κ(X), is bounded byK(X)√minK(D*HD), where the minimum is taken over all non-singular matrices D which commute with J. This bound is attainable and it can be simply computed. Similar results hold for other signature matrices J, like in the discretized Klein—Gordon equation. |