Article
Keywords:
$(1,2)$-inverse; Moore-Penrose inverse; Sherman-Morrison-Woodbury formula; quasidirect sum
Summary:
We present some results on generalized inverses and their application to generalizations of the Sherman-Morrison-Woodbury-type formulae.
References:
                        
[1] A. Ben-Israel, T. N. E. Greville: 
Generalized Inverses: Theory and Applications. Wiley-Interscience, New York, 1974. 
MR 0396607[3] M. Fiedler, T. L. Markham: 
Quasidirect addition of matrices and generalized inverses. Linear Algebra Appl. 191 (1993), 165–182. 
MR 1233470[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 10.1214/aoms/1177729893 | 
MR 0035118[7] M. Woodbury: 
Inverting modified matrices. Memorandum Report 42, Statistical Research group, Princeton 1950. 
MR 0038136