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Remarks on the Sherman-Morrison-Woodbury formulae
Mathematica Bohemica, Tome 128 (2003) no. 3, pp. 253-262
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We present some results on generalized inverses and their application to generalizations of the Sherman-Morrison-Woodbury-type formulae.
We present some results on generalized inverses and their application to generalizations of the Sherman-Morrison-Woodbury-type formulae.
DOI : 10.21136/MB.2003.134181
Classification : 15A09, 15A24
Keywords: $(1, 2)$-inverse; Moore-Penrose inverse; Sherman-Morrison-Woodbury formula; quasidirect sum 
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Fiedler, Miroslav. Remarks on the Sherman-Morrison-Woodbury formulae. Mathematica Bohemica, Tome 128 (2003) no. 3, pp. 253-262. doi: 10.21136/MB.2003.134181

[1] A. Ben-Israel, T. N. E. Greville: Generalized Inverses: Theory and Applications. Wiley-Interscience, New York, 1974. | MR

[2] M. Fiedler: Remarks on the Schur complement. Linear Algebra Appl. 39 (1981), 189–196. | DOI | MR | Zbl

[3] M. Fiedler, T. L. Markham: Quasidirect addition of matrices and generalized inverses. Linear Algebra Appl. 191 (1993), 165–182. | MR

[4] M. Fiedler, T. L. Markham: A characterization of the Moore-Penrose inverse. Linear Algebra Appl. 179 (1993), 129–133. | DOI | MR

[5] G. Marsaglia, G. P. H. Styan: Equalities and inequalities for ranks of matrices. Linear Multilinear Algebra 2 (1974), 269–292. | DOI | MR

[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. | DOI | MR

[7] M. Woodbury: Inverting modified matrices. Memorandum Report 42, Statistical Research group, Princeton 1950. | MR

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