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

K. Appi Reddy; T. Kurmayya

Special Matrices (2015)

  • Volume: 3, Issue: 1, page 155-162, electronic only
  • ISSN: 2300-7451

Abstract

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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.

How to cite

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K. Appi Reddy, and T. Kurmayya. "Moore-Penrose inverses of Gram matrices leaving a cone invariant in an indefinite inner product space." Special Matrices 3.1 (2015): 155-162, electronic only. <http://eudml.org/doc/270907>.

@article{K2015,
abstract = {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.},
author = {K. Appi Reddy, T. Kurmayya},
journal = {Special Matrices},
keywords = {Gram matrix; Moore-Penrose inverse; acute cone; Indefinite inner product space; indefinite inner product space},
language = {eng},
number = {1},
pages = {155-162, electronic only},
title = {Moore-Penrose inverses of Gram matrices leaving a cone invariant in an indefinite inner product space},
url = {http://eudml.org/doc/270907},
volume = {3},
year = {2015},
}

TY - JOUR
AU - K. Appi Reddy
AU - T. Kurmayya
TI - Moore-Penrose inverses of Gram matrices leaving a cone invariant in an indefinite inner product space
JO - Special Matrices
PY - 2015
VL - 3
IS - 1
SP - 155
EP - 162, electronic only
AB - 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.
LA - eng
KW - Gram matrix; Moore-Penrose inverse; acute cone; Indefinite inner product space; indefinite inner product space
UR - http://eudml.org/doc/270907
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. 
  2. [2] A. Berman and R.J. Plemmons, NonnegativeMatrices in theMathematical Sciences, Classics in AppliedMathematics, SIAM, 1994. 
  3. [3] J. Bognar, Indefinite inner product spaces, Springer Verlag, 1974. Zbl0286.46028
  4. [4] A. Cegielski, Obtuse cones and Gram matrices with non-negative inverse, Linear Algebra Appl., 335, 167-181, 2001. Zbl0982.15028
  5. [5] L. Collatz, Functional Analysis and Numerical Mathematics, Academic Press, New York, 1966. 
  6. [6] I. Gohberg, P. Lancaster and L. Rodman, Indefinite Linear Algebra and Applications, Birkhauser, Basel, Boston, Berlin, 2005. 
  7. [7] T. Kurmayya and K.C. Sivakumar, Nonnegative Moore-Penrose inverse of Gram operators, Linear Algebra Appl., 422, 471- 476, 2007. Zbl1122.15007
  8. [8] Ar. Meenakshi and D. Krishnaswamy, Principal pivot transforms of range symmetric matrices in Minkowski space, Tamkang J. Math. 37 211-219 2006. Zbl1182.15016
  9. [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. [10] I.M. Radojevic, New results for EP matrices in indefinite inner product spaces, Czechoslovak Math. J. 64 91-103, 2014. Zbl06391479
  11. [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. Zbl1097.47002
  12. [12] K. Ramanathan and K.C. Sivakumar, Theorems of the alternative order indefinite inner product spaces, J. Optim. Theory Appl., 137 99-104, 2008. Zbl1151.46055
  13. [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. Zbl1176.15007
  14. [14] Sachindranath Jayaraman, EP matrices in indefinite inner product spaces, Funct. Anal. Approx. Comput., 4 23-31, 2012. Zbl1289.46040
  15. [15] Sachindranath Jayaraman, Nonnegative generalized inverses in indefinite inner product spaces, Filomat, 27, 659-670, 2013. 
  16. [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. Zbl1266.15007
  17. [17] K.C. Sivakumar, A new characterization of nonnegativity of Moore-Penrose inverses of Gram operators, Positivity, 13, 277- 286, 2009. Zbl1161.15004

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