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.
@article{bwmeta1.element.doi-10_1515_spma-2015-0013,
author = {K. Appi Reddy and T. Kurmayya},
title = {Moore-Penrose inverses of Gram matrices leaving a cone invariant in an indefinite inner product space},
journal = {Special Matrices},
volume = {3},
year = {2015},
zbl = {06473596},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_spma-2015-0013}
}
K. Appi Reddy; T. Kurmayya. Moore-Penrose inverses of Gram matrices leaving a cone invariant in an indefinite inner product space. Special Matrices, Tome 3 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_spma-2015-0013/
[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. | Zbl 0286.46028
[4] A. Cegielski, Obtuse cones and Gram matrices with non-negative inverse, Linear Algebra Appl., 335, 167-181, 2001. | Zbl 0982.15028
[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. | Zbl 1122.15007
[8] Ar. Meenakshi and D. Krishnaswamy, Principal pivot transforms of range symmetric matrices in Minkowski space, Tamkang J. Math. 37 211-219 2006. | Zbl 1182.15016
[9] M.Z. Petrovic and P.S. Stanimirovic, Representations and computations of {2, 3∼} and {2, 4∼} inverses in indefinite inner product 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. | Zbl 06391479
[11] K. Ramanathan, K. Kamaraj and K.C. Sivakumar, Indefinite product of matrices and applications to indefinite inner product spaces, J. Anal., 12, 135-142, 2004. | Zbl 1097.47002
[12] K. Ramanathan and K.C. Sivakumar, Theorems of the alternative order indefinite inner product spaces, J. Optim. Theory Appl., 137 99-104, 2008. | Zbl 1151.46055
[13] K. Ramanathan and K.C. Sivakumar, Nonnegative Moore-Penrose Inverse of Gram Matrices in an Indefinite Inner Product Space, J. Optim Theory Appl., 140, 189-196, 2009. | Zbl 1176.15007
[14] Sachindranath Jayaraman, EP matrices in indefinite inner product spaces, Funct. Anal. Approx. Comput., 4 23-31, 2012. | Zbl 1289.46040
[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 generalized inverses of matrices, 133-141, Springer, New Delhi, 2013. | Zbl 1266.15007
[17] K.C. Sivakumar, A new characterization of nonnegativity of Moore-Penrose inverses of Gram operators, Positivity, 13, 277- 286, 2009. | Zbl 1161.15004