On block triangular matrices with signed Drazin inverse

Title:

On block triangular matrices with signed Drazin inverse

Creator:

Bu, Changjiang, Wang, Wenzhe, Zhou, Jiang, and Sun, Lizhu

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:75f528dd-9582-4e64-9317-5151d71cd019
uuid:75f528dd-9582-4e64-9317-5151d71cd019

Subject:

sign pattern matrix, signed Drazin inverse, and strong sign nonsingular matrix

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

883-892

Source:

Czechoslovak Mathematical Journal | 2014 Volume:64 | Number:4

Harvested from:

CDK

Metadata only:

false