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Tytuł artykułu

Moore-Penrose inverses of Gram matrices leaving a cone invariant in an indefinite inner product space

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we characterize Moore-Penrose inverses of Gram matrices leaving a cone invariant in an indefinite inner product space using the indefinite matrix multiplication. This characterization includes the acuteness (or obtuseness) of certain closed convex cones.
Wydawca
Czasopismo
Rocznik
Tom
3
Numer
1
Opis fizyczny
Daty
otrzymano
2015-02-19
zaakceptowano
2015-07-02
online
2015-07-10
Twórcy
  • Department of Mathematics, National Institute of Technology Warangal, Warangal - 506 004, India,
autor
  • Department of Mathematics, National Institute of Technology Warangal, Warangal - 506 004, 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, NonnegativeMatrices in theMathematical Sciences, Classics in AppliedMathematics, SIAM,1994.
  • [3] J. Bognar, Indefinite inner product spaces, Springer Verlag, 1974.
  • [4] A. Cegielski, Obtuse cones and Gram matrices with non-negative inverse, Linear Algebra Appl., 335, 167-181, 2001.
  • [5] L. Collatz, Functional Analysis and Numerical Mathematics, Academic Press, New York, 1966.
  • [6] I. Gohberg, P. Lancaster and L. Rodman, Indefinite Linear Algebra and Applications, Birkhauser, Basel, Boston, Berlin, 2005.
  • [7] T. Kurmayya and K.C. Sivakumar, Nonnegative Moore-Penrose inverse of Gram operators, Linear Algebra Appl., 422, 471-476, 2007.
  • [8] Ar. Meenakshi and D. Krishnaswamy, Principal pivot transforms of range symmetric matrices in Minkowski space, TamkangJ. Math. 37 211-219 2006.
  • [9] M.Z. Petrovic and P.S. Stanimirovic, Representations and computations of {2, 3∼} and {2, 4∼} inverses in indefinite innerproduct spaces, Appl. Math. Comput., 254, 157-171, 2015.
  • [10] I.M. Radojevic, New results for EP matrices in indefinite inner product spaces, Czechoslovak Math. J. 64 91-103, 2014.
  • [11] K. Ramanathan, K. Kamaraj and K.C. Sivakumar, Indefinite product of matrices and applications to indefinite inner productspaces, J. Anal., 12, 135-142, 2004.
  • [12] K. Ramanathan and K.C. Sivakumar, Theorems of the alternative order indefinite inner product spaces, J. Optim. TheoryAppl., 137 99-104, 2008.
  • [13] K. Ramanathan and K.C. Sivakumar, Nonnegative Moore-Penrose Inverse of Gram Matrices in an Indefinite Inner ProductSpace, J. Optim Theory Appl., 140, 189-196, 2009.
  • [14] Sachindranath Jayaraman, EP matrices in indefinite inner product spaces, Funct. Anal. Approx. Comput., 4 23-31, 2012.
  • [15] Sachindranath Jayaraman, Nonnegative generalized inverses in indefinite inner product spaces, Filomat, 27, 659-670, 2013.
  • [16] Sachindranath Jayaraman, The reverse order law in indefinite inner product spaces, Combinatorial matrix theory and generalizedinverses of matrices, 133-141, Springer, New Delhi, 2013.
  • [17] K.C. Sivakumar, A new characterization of nonnegativity of Moore-Penrose inverses of Gram operators, Positivity, 13, 277-286, 2009.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_spma-2015-0013
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