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Structure of a nonnegative regular matrix and its generalized inverses

โœ Scribed by R.B. Bapat

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
278 KB
Volume
268
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

A nonnegative matrix is called regular if it admits a nonnegative generalized inverse. The structure of such matrices has been studied by several authors. If A is a nonnegative regular matrix, then we obtain a complete description of all nonnegative generalized inverses of A. In particular, it is shown that if A is a nonnegative regular matrix with no zero row or column, then the zero-nonzero pattern of any nonnegative generalized inverse of A is dominated by that of A r, the transpose of A. We also obtain the structure of nonnegative matrices which admit nonnegative least-squares and minimum-norm generalized inverses.

๐Ÿ“œ SIMILAR VOLUMES

Relationships between generalized invers
Relationships between generalized inverses of a matrix and generalized inverses of its rank-one-modifications
โœ Jerzy K Baksalary; Oskar Maria Baksalary ๐Ÿ“‚ Article ๐Ÿ“… 2004 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 215 KB

For given complex matrix A and nonzero complex vectors b, c, relationships between generalized inverses of A and generalized inverses of the rank-one-modified matrix M = A + bc \* (with c \* being the conjugate transpose of c) are investigated. The following three questions are considered: (i) when