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

Similarity:

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

Similarity:

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

Similarity:

The inertia set of a symmetric sign pattern A is the set i ( A ) = { i ( B ) ∣ B = B T ∈ 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...