| Title:
|
On block triangular matrices with signed Drazin inverse (English) |
| Author:
|
Bu, Changjiang |
| Author:
|
Wang, Wenzhe |
| Author:
|
Zhou, Jiang |
| Author:
|
Sun, Lizhu |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
4 |
| Year:
|
2014 |
| Pages:
|
883-892 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
sign pattern matrix |
| Keyword:
|
signed Drazin inverse |
| Keyword:
|
strong sign nonsingular matrix |
| MSC:
|
15A09 |
| MSC:
|
15B35 |
| idZBL:
|
Zbl 06433702 |
| idMR:
|
MR3304786 |
| DOI:
|
10.1007/s10587-014-0141-6 |
| . |
| Date available:
|
2015-02-09T17:22:35Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144149 |
| . |
| Reference:
|
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| . |
