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The generalized inverse of a nonnegative matrix


Authors: R. J. Plemmons and R. E. Cline
Journal: Proc. Amer. Math. Soc. 31 (1972), 46-50
MSC: Primary 15.15
DOI: https://doi.org/10.1090/S0002-9939-1972-0285541-5
Erratum: Proc. Amer. Math. Soc. 39 (1973), 651.
MathSciNet review: 0285541
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Abstract: Necessary and sufficient conditions are given in order that a nonnegative matrix have a nonnegative Moore-Penrose generalized inverse.


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

  • [1] A. Ben-Israel and A. Charnes, Contributions to the theory of generalized inverses, J. Soc. Indust. Appl. Math. 11 (1963), 667-699. MR 31 #3441. MR 0179192 (31:3441)
  • [2] R. E. Cline, Representations for the generalized inverse of a partitioned matrix, J. Soc. Indust. Appl. Math. 12 (1964), 588-600. MR 30 #3106. MR 0172890 (30:3106)
  • [3] -, Inverses of rank invariant powers of a matrix, SIAM J. Numer. Anal. 5 (1968), 182-197. MR 37 #2769. MR 0227184 (37:2769)
  • [4] D. Z. Djoković, Note on nonnegative matrices, Proc. Amer. Math. Soc. 25 (1970), 80-82. MR 41 #1768. MR 0257114 (41:1768)
  • [5] P. Flor, On groups of nonnegative matrices, Compositio Math. 21 (1969), 376-382. MR 41 #1769. MR 0257115 (41:1769)
  • [6] T. N. E. Greville, Some applications of the pseudo-inverse of a matrix, SIAM Rev. 2 (1960), 15-22. MR 22 #1067. MR 0110185 (22:1067)
  • [7] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc. 51 (1955), 406-413. MR 16, 1082. MR 0069793 (16:1082a)
  • [8] -, On the best approximate solutions of linear matrix equations, Proc. Cambridge Philos. Soc. 52 (1956), 17-19. MR 17, 536. MR 0074092 (17:536d)
  • [9] R. Plemmons, Graphs and nonnegative matrices, Linear Algebra and Appl. (to appear). MR 0313109 (47:1664)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0285541-5
Keywords: Generalized inverse, idempotent matrix, nonnegative matrix, singular values, stochatics matrix
Article copyright: © Copyright 1972 American Mathematical Society

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