Geodesic
Spectral properties of sign symmetric matrices
The electronic journal of linear algebra, Tome 13 (2005), pp. 90-110.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $3\times 3$ 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 $k$, but not all the eigenvalues of $A$ are positive real numbers.
Classification : 15A18, 15A29
Keywords: spectrum, sign symmetric matrices, circulant matrices, basic circulant permutation matrices, P -matrices, P M-matrices, Q-matrices, QM-matrices 
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     author = {Hershkowitz, Daniel and Keller, Nathan},
     title = {Spectral properties of sign symmetric matrices},
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Hershkowitz, Daniel; Keller, Nathan. Spectral properties of sign symmetric matrices. The electronic journal of linear algebra, Tome 13 (2005), pp. 90-110. http://geodesic.mathdoc.fr/item/ELA_2005__13__a19/