Positive splittings of matrices and their nonnegative Moore-Penrose inverses

• Autorzy: Tamminana Kurmayya , Koratti C. Sivakumar
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Moore-Penrose inverse; positive splitting

Kategorie tematyczne

• 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
• 15A09: Matrix inversion, generalized inverses

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2008
• Tom: 28
• Numer: 2
• Strony: 227-235

Daty

wydano

2008

otrzymano

2008-03-02

poprawiono

2008-04-02

poprawiono

2008-06-09

Twórcy

autor

Tamminana Kurmayya

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

autor

Koratti C. Sivakumar

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

Bibliografia

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• [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.
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• [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.

Identyfikatory

DOI

10.7151/dmgaa.1145