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ArticleOriginal scientific text

Title

Positive splittings of matrices and their nonnegative Moore-Penrose inverses

Authors 1, 1

Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Madras, Chennai - 600 036, India

Abstract

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.

Keywords

ENG
Moore-Penrose inverse, positive splitting

Bibliography

  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.
Discussiones Mathematicae - General Algebra and Applications
2008/28/2
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Pages:
227-235
Main language of publication
English
Received
2008-03-02
Accepted
2008-04-02
Published
2008

DOI: 10.7151/dmgaa.1145

Exact and natural sciences