# Article

 Title: The inertia set of nonnegative symmetric sign pattern with zero diagonal (English) Author: Gao, Yubin Author: Shao, Yanling Language: English Journal: Czechoslovak Mathematical Journal ISSN: 0011-4642 (print) ISSN: 1572-9141 (online) Volume: 53 Issue: 4 Year: 2003 Pages: 925-934 Summary lang: English . Category: math . Summary: The inertia set of a symmetric sign pattern $A$ is the set $i(A)=\lbrace i(B) \mid B=B^T \in Q(A)\rbrace$, 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. (English) Keyword: sign pattern Keyword: inertia Keyword: inertia set Keyword: unique inertia MSC: 15A18 idZBL: Zbl 1080.15501 idMR: MR2018840 . Date available: 2009-09-24T11:07:54Z Last updated: 2020-07-03 Stable URL: http://hdl.handle.net/10338.dmlcz/127850 . Reference: [1] B. N. Datta: Stability and inertia.Linear Algebra Appl. 302–303 (1999), 563–600. Zbl 0972.15009, MR 1733550 Reference: [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. MR 1751135 Reference: [3] R. A. Horn and C. R. Johnson: Matrix Analysis.Cambridge University Press, Cambridge, 1985. MR 0832183 Reference: [4] R. A. Brualdi and B. L. Shader: Matrices of Sign-solvable Linear System.Cambridge University Press, Cambridge, 1995. MR 1358133 .

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