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On the Courant-Fischer theory for Krein spaces |
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| Authors: | N Bebiano H Nakazato |
| Institution: | a University of Coimbra, CMUC, Mathematics Department, P 3001-454 Coimbra, Portugal b Hirosaki University, Department of Mathematical Sciences, 036-8561 Hirosaki, Japan c University of Coimbra, Physics Department, P 3004-516 Coimbra, Portugal |
| Abstract: | Let J=Ir⊕-In-r,0<r<n. An n×n complex matrix A is said to be J-Hermitian if JA=A∗J. An extension of the classical theory of Courant and Fischer on the Rayleigh ratio of Hermitian matrices is stated for J-Hermitian matrices. Applications to the theory of small oscilations of a mechanical system are presented. |
| Keywords: | 47A12 46C20 58F05 |
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