Remarks on the Sherman-Morrison-Woodbury formulae

Miroslav Fiedler

Mathematica Bohemica (2003)

  • Volume: 128, Issue: 3, page 253-262
  • ISSN: 0862-7959

Abstract

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We present some results on generalized inverses and their application to generalizations of the Sherman-Morrison-Woodbury-type formulae.

How to cite

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Fiedler, Miroslav. "Remarks on the Sherman-Morrison-Woodbury formulae." Mathematica Bohemica 128.3 (2003): 253-262. <http://eudml.org/doc/249238>.

@article{Fiedler2003,
abstract = {We present some results on generalized inverses and their application to generalizations of the Sherman-Morrison-Woodbury-type formulae.},
author = {Fiedler, Miroslav},
journal = {Mathematica Bohemica},
keywords = {$(1,2)$-inverse; Moore-Penrose inverse; Sherman-Morrison-Woodbury formula; quasidirect sum; -inverse; Moore-Penrose inverse; Sherman-Morrison-Woodbury formula; quasidirect sum},
language = {eng},
number = {3},
pages = {253-262},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Remarks on the Sherman-Morrison-Woodbury formulae},
url = {http://eudml.org/doc/249238},
volume = {128},
year = {2003},
}

TY - JOUR
AU - Fiedler, Miroslav
TI - Remarks on the Sherman-Morrison-Woodbury formulae
JO - Mathematica Bohemica
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 128
IS - 3
SP - 253
EP - 262
AB - We present some results on generalized inverses and their application to generalizations of the Sherman-Morrison-Woodbury-type formulae.
LA - eng
KW - $(1,2)$-inverse; Moore-Penrose inverse; Sherman-Morrison-Woodbury formula; quasidirect sum; -inverse; Moore-Penrose inverse; Sherman-Morrison-Woodbury formula; quasidirect sum
UR - http://eudml.org/doc/249238
ER -

References

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  1. Generalized Inverses: Theory and Applications, Wiley-Interscience, New York, 1974. (1974) MR0396607
  2. 10.1016/0024-3795(81)90302-5, Linear Algebra Appl. 39 (1981), 189–196. (1981) Zbl0465.15004MR0625249DOI10.1016/0024-3795(81)90302-5
  3. Quasidirect addition of matrices and generalized inverses, Linear Algebra Appl. 191 (1993), 165–182. (1993) MR1233470
  4. 10.1016/0024-3795(93)90325-I, Linear Algebra Appl. 179 (1993), 129–133. (1993) MR1200147DOI10.1016/0024-3795(93)90325-I
  5. 10.1080/03081087408817070, Linear Multilinear Algebra 2 (1974), 269–292. (1974) MR0384840DOI10.1080/03081087408817070
  6. 10.1214/aoms/1177729893, Ann. Math. Statist. 21 (1950), 124. (1950) MR0035118DOI10.1214/aoms/1177729893
  7. Inverting modified matrices, Memorandum Report 42, Statistical Research group, Princeton 1950. MR0038136

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