| Title:
|
Remarks on the Sherman-Morrison-Woodbury formulae (English) |
| Author:
|
Fiedler, Miroslav |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
128 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
253-262 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present some results on generalized inverses and their application to generalizations of the Sherman-Morrison-Woodbury-type formulae. (English) |
| Keyword:
|
$(1,2)$-inverse |
| Keyword:
|
Moore-Penrose inverse |
| Keyword:
|
Sherman-Morrison-Woodbury formula |
| Keyword:
|
quasidirect sum |
| MSC:
|
15A09 |
| MSC:
|
15A24 |
| idZBL:
|
Zbl 1055.15007 |
| idMR:
|
MR2012603 |
| DOI:
|
10.21136/MB.2003.134181 |
| . |
| Date available:
|
2009-09-24T22:09:28Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134181 |
| . |
| Reference:
|
[1] A. Ben-Israel, T. N. E. Greville: Generalized Inverses: Theory and Applications.Wiley-Interscience, New York, 1974. MR 0396607 |
| Reference:
|
[2] M. Fiedler: Remarks on the Schur complement.Linear Algebra Appl. 39 (1981), 189–196. Zbl 0465.15004, MR 0625249, 10.1016/0024-3795(81)90302-5 |
| Reference:
|
[3] M. Fiedler, T. L. Markham: Quasidirect addition of matrices and generalized inverses.Linear Algebra Appl. 191 (1993), 165–182. MR 1233470 |
| Reference:
|
[4] M. Fiedler, T. L. Markham: A characterization of the Moore-Penrose inverse.Linear Algebra Appl. 179 (1993), 129–133. MR 1200147, 10.1016/0024-3795(93)90325-I |
| Reference:
|
[5] G. Marsaglia, G. P. H. Styan: Equalities and inequalities for ranks of matrices.Linear Multilinear Algebra 2 (1974), 269–292. MR 0384840, 10.1080/03081087408817070 |
| Reference:
|
[6] J. Sherman, W. J. Morrison: Adjustment of an inverse matrix corresponding to a change in one element of a given matrix.Ann. Math. Statist. 21 (1950), 124. MR 0035118, 10.1214/aoms/1177729893 |
| Reference:
|
[7] M. Woodbury: Inverting modified matrices.Memorandum Report 42, Statistical Research group, Princeton 1950. MR 0038136 |
| . |
