Perturbation theory for the eigenvalues of factorised symmetric matrices

✍ Scribed by K. Veselić

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 127 KB
• Volume: 309
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(99)00157-3

✦ Synopsis

We obtain eigenvalue perturbation results for a factorised Hermitian matrix H = GJ G * where J 2 = I and G has full row rank and is perturbed into G + δG, where δG is small with respect to G. This complements the earlier results on the easier case of G with full column rank. Applied to square factors G our results help to identify the so-called quasidefinite matrices as a natural class on which the relative perturbation theory for the eigensolution can be formulated in a way completely analogous to the one already known for positive definite matrices.