Rank of a difference of matrices and associated generalized inverses
Journal Article
·
· Linear Algebra Its Appl.; (United States)
- Univ. of Tennessee, Knoxville
Various representations are given to characterize the rank of A-S in terms of rank A + k, where A and S are arbitrary complex matrices and k is a function of A and S. It is shown that, if S = AMA for some matrix M, and if G is any matrix satisfying A = AGA, then rank(A-S) = rank A - nullity (I-SG). Several alternative forms of this result are established, as are many equivalent conditions to have rank(A-S) = rank A - rank S. General forms for the Moore-Penrose inverse of matrices A-S are developed, which include as special cases various results by Penrose, Wedin, Hartwig, and others. 1 figure.
- DOE Contract Number:
- W-7405-ENG-26
- OSTI ID:
- 7182531
- Journal Information:
- Linear Algebra Its Appl.; (United States), Journal Name: Linear Algebra Its Appl.; (United States) Vol. 24; ISSN LAAPA
- Country of Publication:
- United States
- Language:
- English
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