The inertia set of nonnegative symmetric sign pattern with zero diagonal

Yubin Gao; Yan Ling Shao

Displaying similar documents to “The inertia set of nonnegative symmetric sign pattern with zero diagonal”

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.

On block triangular matrices with signed Drazin inverse

Changjiang Bu, Wenzhe Wang, Jiang Zhou, Lizhu Sun (2014)

Czechoslovak Mathematical Journal

Similarity:

The sign pattern of a real matrix $A$ , denoted by $sgn A$ , is the $(+, -, 0)$ -matrix obtained from $A$ by replacing each entry by its sign. Let $𝒬 (A)$ denote the set of all real matrices $B$ such that $sgn B = sgn A$ . For a square real matrix $A$ , the Drazin inverse of $A$ is the unique real matrix $X$ such that $A^{k + 1} X = A^{k}$ , $X A X = X$ and $A X = X A$ , where $k$ is the Drazin index of $A$ . We say that $A$ has signed Drazin inverse if $sgn {\tilde{A}}^{d} = sgn A^{d}$ for any $\tilde{A} \in 𝒬 (A)$ , where $A^{d}$ denotes the Drazin inverse of $A$ . In this paper, we give necessary conditions for some block triangular matrices...

On the inertia sets of some symmetric sign patterns

C. M. da Fonseca (2006)

Czechoslovak Mathematical Journal

Similarity:

A matrix whose entries consist of elements from the set ${+, -, 0}$ is a sign pattern matrix. Using a linear algebra theoretical approach we generalize of some recent results due to Hall, Li and others involving the inertia of symmetric tridiagonal sign matrices.