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##### On the Courant-Fisher theory for Krein spaces

**Authors**: N. BEBIANO, H. NAKAZATO and J. DA PROVIDÃŠNCIA

**Ref.**: Linear Algebra and its Applications **430**, 1867-1876 (2009)

**Abstract**: Let J = I-r circle plus -In-r, 0 < r < n. An n x 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