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

References

[1] A. Ben-Israel and T.N.E., Greville, Generalized Inverses:Theory and Applications, 2nd edition, Springer Verlag, New York, 2003. Search in Google Scholar

[2] A. Berman and R.J. Plemmons, NonnegativeMatrices in theMathematical Sciences, Classics in AppliedMathematics, SIAM, 1994. 10.1137/1.9781611971262Search in Google Scholar

[3] J. Bognar, Indefinite inner product spaces, Springer Verlag, 1974. 10.1007/978-3-642-65567-8Search in Google Scholar

[4] A. Cegielski, Obtuse cones and Gram matrices with non-negative inverse, Linear Algebra Appl., 335, 167-181, 2001. 10.1016/S0024-3795(01)00284-1Search in Google Scholar

[5] L. Collatz, Functional Analysis and Numerical Mathematics, Academic Press, New York, 1966. Search in Google Scholar

[6] I. Gohberg, P. Lancaster and L. Rodman, Indefinite Linear Algebra and Applications, Birkhauser, Basel, Boston, Berlin, 2005. 10.1007/s00020-005-1356-6Search in Google Scholar

[7] T. Kurmayya and K.C. Sivakumar, Nonnegative Moore-Penrose inverse of Gram operators, Linear Algebra Appl., 422, 471- 476, 2007. 10.1016/j.laa.2006.11.004Search in Google Scholar

[8] Ar. Meenakshi and D. Krishnaswamy, Principal pivot transforms of range symmetric matrices in Minkowski space, Tamkang J. Math. 37 211-219 2006. 10.5556/j.tkjm.37.2006.166Search in Google Scholar

[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. Search in Google Scholar

[10] I.M. Radojevic, New results for EP matrices in indefinite inner product spaces, Czechoslovak Math. J. 64 91-103, 2014. 10.1007/s10587-014-0086-9Search in Google Scholar

[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. Search in Google Scholar

[12] K. Ramanathan and K.C. Sivakumar, Theorems of the alternative order indefinite inner product spaces, J. Optim. Theory Appl., 137 99-104, 2008. 10.1007/s10957-007-9321-ySearch in Google Scholar

[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. 10.1007/s10957-008-9450-ySearch in Google Scholar

[14] Sachindranath Jayaraman, EP matrices in indefinite inner product spaces, Funct. Anal. Approx. Comput., 4 23-31, 2012. Search in Google Scholar

[15] Sachindranath Jayaraman, Nonnegative generalized inverses in indefinite inner product spaces, Filomat, 27, 659-670, 2013. 10.2298/FIL1304659JSearch in Google Scholar

[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. 10.1007/978-81-322-1053-5_11Search in Google Scholar

[17] K.C. Sivakumar, A new characterization of nonnegativity of Moore-Penrose inverses of Gram operators, Positivity, 13, 277- 286, 2009. 10.1007/s11117-008-2167-1Search in Google Scholar