Outer inverses: Jacobi type identities and nullities of submatrices

Bapat, R. B. (2003) Outer inverses: Jacobi type identities and nullities of submatrices Linear Algebra and its Applications, 361 . pp. 107-120. ISSN 0024-3795

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Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1016/S0024-3795(02)00317-8


According to the Jacobi identity, if A is an invertible matrix then any minor of A-1 equals, up to a sign, the determinant of A-1 times the complementary minor in the transpose of A. The identity is extended to any outer inverse, thereby generalizing several results in the literature for special generalized inverses. A permanental analog of the Jacobi identity is proved. Bounds are obtained for the difference between the nullity of a submatrix of A and that of the complementary submatrix in any generalized inverse or an outer inverse of A. The result extends earlier work of Fiedler, Markham and Gustafson for the inverse and of Robinson for the Moore-Penrose inverse.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Jacobi Identity; Outer Inverse; Generalized Inverse; Permanent; Nullity of a Submatrix
ID Code:78317
Deposited On:19 Jan 2012 06:32
Last Modified:19 Jan 2012 06:32

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