On the inertia sets of some symmetric sign patterns

C. M. da Fonseca

Displaying similar documents to “On the inertia sets of some symmetric sign patterns”

When does the inverse have the same sign pattern as the transpose?

Carolyn A. Eschenbach, Frank J. Hall, Deborah L. Harrell, Zhongshan Li (1999)

Czechoslovak Mathematical Journal

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By a sign pattern (matrix) we mean an array whose entries are from the set ${+, -, 0}$ . The sign patterns $A$ for which every real matrix with sign pattern $A$ has the property that its inverse has sign pattern $A^{T}$ are characterized. Sign patterns $A$ for which some real matrix with sign pattern $A$ has that property are investigated. Some fundamental results as well as constructions concerning such sign pattern matrices are provided. The relation between these sign patterns and the sign patterns of orthogonal...

Symmetric sign patterns with maximal inertias

In-Jae Kim, Charles Waters (2010)

Czechoslovak Mathematical Journal

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The inertia of an $n$ by $n$ symmetric sign pattern is called maximal when it is not a proper subset of the inertia of another symmetric sign pattern of order $n$ . In this note we classify all the maximal inertias for symmetric sign patterns of order $n$ , and identify symmetric sign patterns with maximal inertias by using a rank-one perturbation.

The inertia set of nonnegative symmetric sign pattern with zero diagonal

Yubin Gao, Yan Ling Shao (2003)

Czechoslovak Mathematical Journal

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The inertia set of a symmetric sign pattern $A$ is the set $i (A) = {i (B) ∣ B = B^{T} \in Q (A)}$ , 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...

Pattern avoidance in matrices.

Kitaev, Sergey, Mansour, Toufik, Vella, Antoine (2005)

Journal of Integer Sequences [electronic only]

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Essential sign change numbers of full sign pattern matrices

Xiaofeng Chen, Wei Fang, Wei Gao, Yubin Gao, Guangming Jing, Zhongshan Li, Yanling Shao, Lihua Zhang (2016)

Special Matrices

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A sign pattern (matrix) is a matrix whose entries are from the set {+, −, 0} and a sign vector is a vector whose entries are from the set {+, −, 0}. A sign pattern or sign vector is full if it does not contain any zero entries. The minimum rank of a sign pattern matrix A is the minimum of the ranks of the real matrices whose entries have signs equal to the corresponding entries of A. The notions of essential row sign change number and essential column sign change number are introduced...