Spectral properties of sign symmetric matrices
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Spectral properties of sign symmetric matrices are studied.A criterion for sign symmetry of shifted basic circulant permutation matrices is proven, and is then used to answer the question which complex numbers can serve as eigenvalues of sign symmetric 3 × 3 matrices. The results are applied in the discussion of the eigenvalues of QM-matrices.In particular, it is shown that for every positive integer n there exists a QM-matrix A such that Ak is a sign symmetric P-matrix for all k ≤ n, but not all the eigenvalues of A are positive real numbers.
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