Abstract
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 A k is a sign symmetric P-matrix for all k ≤ n, but not all the eigenvalues of A are positive real numbers.
Original language | English |
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Journal | Electronic Journal of Linear Algebra |
Volume | 13 |
DOIs | |
State | Published - 11 Mar 2005 |
Externally published | Yes |
Keywords
- Basic circulant permutation matrices
- Circulant matrices
- P-matrices
- PM-matrices
- Q-matrices
- QM-matrices
- Sign symmetric matrices
- Spectrum