Positive splittings of matrices and their nonnegative Moore-Penrose inverses

Tamminana Kurmayya; Koratti C. Sivakumar

Discussiones Mathematicae - General Algebra and Applications (2008)

  • Volume: 28, Issue: 2, page 227-235
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Tamminana Kurmayya, and Koratti C. Sivakumar. "Positive splittings of matrices and their nonnegative Moore-Penrose inverses." Discussiones Mathematicae - General Algebra and Applications 28.2 (2008): 227-235. <http://eudml.org/doc/276915>.

@article{TamminanaKurmayya2008,
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.},
author = {Tamminana Kurmayya, Koratti C. Sivakumar},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {Moore-Penrose inverse; positive splitting; nonnegativity},
language = {eng},
number = {2},
pages = {227-235},
title = {Positive splittings of matrices and their nonnegative Moore-Penrose inverses},
url = {http://eudml.org/doc/276915},
volume = {28},
year = {2008},
}

TY - JOUR
AU - Tamminana Kurmayya
AU - Koratti C. Sivakumar
TI - Positive splittings of matrices and their nonnegative Moore-Penrose inverses
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2008
VL - 28
IS - 2
SP - 227
EP - 235
AB - 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.
LA - eng
KW - Moore-Penrose inverse; positive splitting; nonnegativity
UR - http://eudml.org/doc/276915
ER -

References

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  1. [1] A. Ben-Israel and T.N.E. Greville, Generalized Inverses: Theory and Applications, 2nd edition, Springer Verlag, New York 2003. Zbl1026.15004
  2. [2] A. Berman and R.J. Plemmons, Monotonocity and the generalized inverse, SIAM J. Appl. Math. 22 (1972), 155-161. Zbl0255.15005
  3. [3] A. Berman and R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Classics in Applied Mathematics, SIAM 1994. Zbl0815.15016
  4. [4] L. Collatz, Functional Analysis and Numerical Mathematics, Academic, New York 1966. 
  5. [5] M.I. Gil, On positive invertibility of matrices, Positivity 2 (1998), 65-170. Zbl0908.15003
  6. [6] M.I. Gil, On invertibility and positive invertibility of matrices, Lin. Alg. Appl. 327 (2001), 95-104. Zbl0978.15004
  7. [7] M.A. Krasnosel'skij, J.A. Lifshits and A.V. Sobolev, Positive linear systems, Heldermann Verlag, Berlin 1989. 
  8. [8] T. Kurmayya, Nonnegative Moore-Penrose inverses of operators between Hilbert spaces, Ph.D. Dissertation, Indian Institute of Technology Madras, Submitted, December 2007. Zbl1122.15007
  9. [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. Zbl1169.47003
  10. [10] O.L. Mangasarian, Characterizations of real matrices of monotone kind, SIAM. Rev. 10 (1968), 439-441. Zbl0179.05102
  11. [11] J.E. Peris, A new characterization of inverse-positive matrices, Lin. Alg. Appl. 154-156 (1991), 45-58. 
  12. [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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