Geodesic
Special forms of generalized inverses of row block matrices
The electronic journal of linear algebra, Tome 13 (2005), pp. 249-261.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Given a row block matrix [ A, B ], this paper investigates the relations between the generalized inverse [ A, B ]- and the column block matrix u* A-B- y" consisting of two generalized inverses A- and B-. The first step of the investigation is to establish a formula for the minimal rank of the difference [ A, B ]- - u* A-B- y", the second step is to find a necessary and sufficient condition for [ A, B ]- = u* A-B- y" to hold by letting the minimal rank be zero. Seven types of generalized inverses of matrices are taken into account.
Classification : 15A03, 15A09
Keywords: block matrix, generalized inverse, minimal rank formula, Moore-Penrose inverse, Schur complement 
@article{ELA_2005__13__a7,
     author = {Tian, Yongge},
     title = {Special forms of generalized inverses of row block matrices},
     journal = {The electronic journal of linear algebra},
     pages = {249--261},
     publisher = {mathdoc},
     volume = {13},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2005__13__a7/}
}
TY  - JOUR
AU  - Tian, Yongge
TI  - Special forms of generalized inverses of row block matrices
JO  - The electronic journal of linear algebra
PY  - 2005
SP  - 249
EP  - 261
VL  - 13
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ELA_2005__13__a7/
LA  - en
ID  - ELA_2005__13__a7
ER  - 
%0 Journal Article
%A Tian, Yongge
%T Special forms of generalized inverses of row block matrices
%J The electronic journal of linear algebra
%D 2005
%P 249-261
%V 13
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ELA_2005__13__a7/
%G en
%F ELA_2005__13__a7
Tian, Yongge. Special forms of generalized inverses of row block matrices. The electronic journal of linear algebra, Tome 13 (2005), pp. 249-261. http://geodesic.mathdoc.fr/item/ELA_2005__13__a7/