A bound for the condition of a hyperbolic eigenvector matrix

The hyperbolic eigenvector matrix is a matrix X which simultaneously diagon alizes the pair (H,J), where H is Hermitian positive definite and J = diag( +/-1) such that X*HX = Delta and X*JX = J, We prove that the spectral condi tion of X, kappa(X), is bounded by kappa(X) less than or equal to root min kappa(D-HD), where the minimum is taken over all non-singular matrices D wh ich commute with J. This bound is attainable and it can be simply computed, Similar results hold for other signature matrices J, like in the discretiz ed Klein-Gordon equation. (C) 1999 Published by Elsevier Science Inc. All r ights reserved.