On spectrum and approximations of one class of sign-symmetric matrices

Details On spectrum and approximations of one class of sign-symmetric matrices On spectrum and approximations of one class of sign-symmetric matrices

2009-05-23

arxiv.org/abs/0905.3799v1

Mathematics

Spectral Theory

24 pages

Scientific paper

A new class of sign-symmetric matrices is introduced in this paper. Such matrices are named J--sign-symmetric. The spectrum of a J--sign-symmetric irreducible matrix is studied under assumptions that its second compound matrix is also J--sign-symmetric and irreducible. The conditions, when such matrices have complex eigenvalues on the largest spectral circle, are given. The existence of two positive simple eigenvalues $\lambda_1 > \lambda_2 > 0$ of a J--sign-symmetric irreducible matrix A is proved under some additional conditions. The question, when the approximation of a J--sign-symmetric matrix with a J--sign-symmetric second compound matrix by strictly J--sign-symmetric matrices with strictly J--sign-symmetric compound matrices is possible, is also studied in this paper.

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