Nonnegative rectangular matrices having certain nonnegative weighted group inverses
Author:
S. K. Jain
Journal:
Proc. Amer. Math. Soc. 85 (1982), 19
MSC:
Primary 15A09; Secondary 15A48
MathSciNet review:
647886
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Abstract: Nonnegative rectangular matrices having nonnegative weighted group inverses are characterized. Our techniques suggest an interesting approach to extend the earlier known results on monotone square matrices to rectangular ones. We also answer a question of characterizing nonnegative matrices having a nonnegative solution where (1) , (2) , (3) is 0symmetric, (4) is 0symmetric. In particular, we obtain theorems of BermanPlemmons and PlemmonsCline characterizing nonnegative matrices with a nonnegative MoorePenrose inverse. Matrices having nonnegative generalized inverses are of interest in the study of finding nonnegative best approximate solutions of linear systems. Such matrices are of considerable interest in statistics, numerical linear algebra and mathematical economics.
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 R. J. Plemmons and R. E. Cline, The generalized inverse of a nonnegative matrix, Proc. Amer. Math. Soc. 31 (1972), 4650. MR 0285541 (44:2759)
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 P. Flor, On groups of nonnegative matrices, Compositio Math. 21 (1969), 376382. MR 0257115 (41:1769)
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 S. K. Jain and L. E. Snyder, Nonnegative monotone matrices, SIAM J. Algebraic Discrete Methods 2 (1981), 6676. MR 604512 (82e:15002)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198206478862
PII:
S 00029939(1982)06478862
Keywords:
Nonnegative matrices,
weighted group inverse
Article copyright:
© Copyright 1982
American Mathematical Society
