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Transactions of the American Mathematical Society

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Decomposition of nonnegative group-monotone matrices

Authors: S. K. Jain, Edward K. Kwak and V. K. Goel
Journal: Trans. Amer. Math. Soc. 257 (1980), 371-385
MSC: Primary 15A09; Secondary 15A23, 15A48
MathSciNet review: 552264
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Abstract: A decomposition of nonnegative matrices with nonnegative group inverses has been obtained. This decomposition provides a new approach to the solution of problems relating to nonnegative matrices with nonnegative group inverses. As a consequence, a number of results are derived. Our results, among other things, answer a question of Berman, extend the theorems of Berman and Plemmons, DeMarr and Flor.

References [Enhancements On Off] (What's this?)

  • [1] A. Ben-Israel and T. N. E. Greville, Generalized inverses: Theory and applications, Wiley, New York, 1974. MR 0396607 (53:469)
  • [2] A. Berman, Nonnegative matrices which are equal to their generalized inverse, Linear Algebra and Appl. 9 (1974), 261-265. MR 0352143 (50:4630)
  • [3] A. Berman and R. J. Plemmons, Matrix group monotonicity, Proc. Amer. Math. Soc. 46 (1974), 355-359. MR 0352116 (50:4603)
  • [4] R. Cline, Inverses of rank invariant powers of a matrix, SIAM J. Numer. Anal. 5 (1968), 182-197. MR 37 #2769. MR 0227184 (37:2769)
  • [5] R. DeMarr, Nonnegative idempotent matrices, Proc. Amer. Math. Soc. 45 (1974), 185-188. MR 0354738 (50:7215)
  • [6] P. Flor, On groups of nonnegative matrices, Compositio Math. 21 (1969), 376-382. MR 0257115 (41:1769)
  • [7] S. K. Jain, V. K. Goel and Edward K. Kwak, Nonnegative matrices having same nonnegative Moore-Penrose and group inverses, Linear and Multilinear Algebra 7 (1979), 59-72. MR 523649 (80f:15007)
  • [8] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc. 51 (1955), 406-413. MR 0069793 (16:1082a)

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