Geodesic
On block triangular matrices with signed Drazin inverse
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 4, pp. 883-892 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.1007/s10587-014-0141-6
Classification : 15A09, 15B35
Keywords: sign pattern matrix; signed Drazin inverse; strong sign nonsingular matrix 
@article{10_1007_s10587_014_0141_6,
     author = {Bu, Changjiang and Wang, Wenzhe and Zhou, Jiang and Sun, Lizhu},
     title = {On block triangular matrices with signed {Drazin} inverse},
     journal = {Czechoslovak Mathematical Journal},
     pages = {883--892},
     year = {2014},
     volume = {64},
     number = {4},
     doi = {10.1007/s10587-014-0141-6},
     mrnumber = {3304786},
     zbl = {06433702},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0141-6/}
}
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
SP  - 883
EP  - 892
VL  - 64
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0141-6/
DO  - 10.1007/s10587-014-0141-6
LA  - en
ID  - 10_1007_s10587_014_0141_6
ER  - 
%0 Journal Article
%A Bu, Changjiang
%A Wang, Wenzhe
%A Zhou, Jiang
%A Sun, Lizhu
%T On block triangular matrices with signed Drazin inverse
%J Czechoslovak Mathematical Journal
%D 2014
%P 883-892
%V 64
%N 4
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0141-6/
%R 10.1007/s10587-014-0141-6
%G en
%F 10_1007_s10587_014_0141_6
Bu, Changjiang; Wang, Wenzhe; Zhou, Jiang; Sun, Lizhu. On block triangular matrices with signed Drazin inverse. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 4, pp. 883-892. doi: 10.1007/s10587-014-0141-6

Cité par Sources :