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2008 | 28 | 2 | 227-235
Tytuł artykułu

Positive splittings of matrices and their nonnegative Moore-Penrose inverses

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In this short note we study necessary and sufficient conditions for the nonnegativity of the Moore-Penrose inverse of a real matrix in terms of certain spectral property shared by all positive splittings of the given matrix.
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Twórcy
  • Department of Mathematics, Indian Institute of Technology, Madras, Chennai - 600 036, India
  • Department of Mathematics, Indian Institute of Technology, Madras, Chennai - 600 036, India
Bibliografia
  • [1] A. Ben-Israel and T.N.E. Greville, Generalized Inverses: Theory and Applications, 2nd edition, Springer Verlag, New York 2003.
  • [2] A. Berman and R.J. Plemmons, Monotonocity and the generalized inverse, SIAM J. Appl. Math. 22 (1972), 155-161.
  • [3] A. Berman and R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Classics in Applied Mathematics, SIAM 1994.
  • [4] L. Collatz, Functional Analysis and Numerical Mathematics, Academic, New York 1966.
  • [5] M.I. Gil, On positive invertibility of matrices, Positivity 2 (1998), 65-170.
  • [6] M.I. Gil, On invertibility and positive invertibility of matrices, Lin. Alg. Appl. 327 (2001), 95-104.
  • [7] M.A. Krasnosel'skij, J.A. Lifshits and A.V. Sobolev, Positive linear systems, Heldermann Verlag, Berlin 1989.
  • [8] T. Kurmayya, Nonnegative Moore-Penrose inverses of operators between Hilbert spaces, Ph.D. Dissertation, Indian Institute of Technology Madras, Submitted, December 2007.
  • [9] T. Kurmayya and K.C. Sivakumar, Nonnegative Moore-Penrose inverses of operators over Hilbert spaces, Positivity, Online First, DOI 10.1007/s11117-007-2173-8.
  • [10] O.L. Mangasarian, Characterizations of real matrices of monotone kind, SIAM. Rev. 10 (1968), 439-441.
  • [11] J.E. Peris, A new characterization of inverse-positive matrices, Lin. Alg. Appl. 154-156 (1991), 45-58.
  • [12] M. Weber, On the Positiveness of the Inverse Operator, Math. Nachr. 163 (1993), 14-5-149. Erratum, Math. Nachr. 171 (1995), 325-326.
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1145
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