On block triangular matrices with signed Drazin inverse

Bu, Changjiang, et al. "On block triangular matrices with signed Drazin inverse." Czechoslovak Mathematical Journal 64.4 (2014): 883-892. <http://eudml.org/doc/269852>.

@article{Bu2014,
abstract = {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.},
author = {Bu, Changjiang, Wang, Wenzhe, Zhou, Jiang, Sun, Lizhu},
journal = {Czechoslovak Mathematical Journal},
keywords = {sign pattern matrix; signed Drazin inverse; strong sign nonsingular matrix; sign pattern matrix; signed Drazin inverse; strong sign nonsingular matrix},
language = {eng},
number = {4},
pages = {883-892},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On block triangular matrices with signed Drazin inverse},
url = {http://eudml.org/doc/269852},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Bu, Changjiang
AU - Wang, Wenzhe
AU - Zhou, Jiang
AU - Sun, Lizhu
TI - On block triangular matrices with signed Drazin inverse
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 4
SP - 883
EP - 892
AB - 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.
LA - eng
KW - sign pattern matrix; signed Drazin inverse; strong sign nonsingular matrix; sign pattern matrix; signed Drazin inverse; strong sign nonsingular matrix
UR - http://eudml.org/doc/269852
ER -