×

zbMATH — the first resource for mathematics

The inertia set of nonnegative symmetric sign pattern with zero diagonal. (English) Zbl 1080.15501
Summary: The inertia set of a symmetric sign pattern \(A\) is the set \(i(A)=\{i(B) \mid B=B^T \in Q(A)\}\), where \(i(B)\)  denotes the inertia of real symmetric matrix  \(B\), and \(Q(A)\) denotes the sign pattern class of  \(A\). In this paper, a complete characterization on the inertia set of the nonnegative symmetric sign pattern \(A\) in which each diagonal entry is zero and all off-diagonal entries are positive is obtained. Further, we also consider the bound for the numbers of nonzero entries in the nonnegative symmetric sign patterns  \(A\) with zero diagonal that require unique inertia.

MSC:
15A18 Eigenvalues, singular values, and eigenvectors
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] B. N. Datta: Stability and inertia. Linear Algebra Appl. 302-303 (1999), 563-600. · Zbl 0972.15009 · doi:10.1016/S0024-3795(99)00213-X
[2] J. H. Drew, C. R. Johnson, D. D. Olesky and P. van den Driessche: Spectrally arbitrary patterns. Linear Algebra Appl. 308 (2000), 121-137. · Zbl 0957.15012
[3] R. A. Horn and C. R. Johnson: Matrix Analysis. Cambridge University Press, Cambridge, 1985. · Zbl 0576.15001
[4] R. A. Brualdi and B. L. Shader: Matrices of Sign-solvable Linear System. Cambridge University Press, Cambridge, 1995. · Zbl 0833.15002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.