New results for EP matrices in indefinite inner product spaces

Ivana M. Radojević

Czechoslovak Mathematical Journal (2014)

  • Volume: 64, Issue: 1, page 91-103
  • ISSN: 0011-4642

Abstract

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In this paper we study J -EP matrices, as a generalization of EP-matrices in indefinite inner product spaces, with respect to indefinite matrix product. We give some properties concerning EP and J -EP matrices and find connection between them. Also, we present some results for reverse order law for Moore-Penrose inverse in indefinite setting. Finally, we deal with the star partial ordering and improve some results given in the “EP matrices in indefinite inner product spaces” (2012), by relaxing some conditions.

How to cite

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Radojević, Ivana M.. "New results for EP matrices in indefinite inner product spaces." Czechoslovak Mathematical Journal 64.1 (2014): 91-103. <http://eudml.org/doc/262015>.

@article{Radojević2014,
abstract = {In this paper we study $J$-EP matrices, as a generalization of EP-matrices in indefinite inner product spaces, with respect to indefinite matrix product. We give some properties concerning EP and $J$-EP matrices and find connection between them. Also, we present some results for reverse order law for Moore-Penrose inverse in indefinite setting. Finally, we deal with the star partial ordering and improve some results given in the “EP matrices in indefinite inner product spaces” (2012), by relaxing some conditions.},
author = {Radojević, Ivana M.},
journal = {Czechoslovak Mathematical Journal},
keywords = {EP matrix; indefinite matrix product; reverse order law; partial order; indefinite inner product space; EP matrix; indefinite matrix product; reverse order law; partial order; indefinite inner product space; Moore-Penrose inverse},
language = {eng},
number = {1},
pages = {91-103},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {New results for EP matrices in indefinite inner product spaces},
url = {http://eudml.org/doc/262015},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Radojević, Ivana M.
TI - New results for EP matrices in indefinite inner product spaces
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 1
SP - 91
EP - 103
AB - In this paper we study $J$-EP matrices, as a generalization of EP-matrices in indefinite inner product spaces, with respect to indefinite matrix product. We give some properties concerning EP and $J$-EP matrices and find connection between them. Also, we present some results for reverse order law for Moore-Penrose inverse in indefinite setting. Finally, we deal with the star partial ordering and improve some results given in the “EP matrices in indefinite inner product spaces” (2012), by relaxing some conditions.
LA - eng
KW - EP matrix; indefinite matrix product; reverse order law; partial order; indefinite inner product space; EP matrix; indefinite matrix product; reverse order law; partial order; indefinite inner product space; Moore-Penrose inverse
UR - http://eudml.org/doc/262015
ER -

References

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  2. Ben-Israel, A., Greville, T. N. E., Generalized Inverses. Theory and Applications. 2nd ed, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC 15 Springer, New York (2003). (2003) Zbl1026.15004MR1987382
  3. Djordjević, D. S., Rakočević, V., Lectures on Generalized Inverses, University of Niš, Faculty of Sciences and Mathematics, Niš (2008). (2008) MR2472376
  4. Drazin, M. P., 10.1090/S0002-9904-1978-14442-5, Bull. Am. Math. Soc. 84 (1978), 139-141. (1978) Zbl0395.20044MR0486234DOI10.1090/S0002-9904-1978-14442-5
  5. Gohberg, I., Lancaster, P., Rodman, L., Indefinite Linear Algebra and Applications, Birkhäuser Basel (2005). (2005) Zbl1084.15005MR2186302
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  7. Jayaraman, S., EP matrices in indefinite inner product spaces, Funct. Anal. Approx. Comput. 4 (2012), 23-31. (2012) MR3087547
  8. Kamaraj, K., Ramanathan, K., Sivakumar, K. C., Indefinite product of matrices and applications to indefinite inner product spaces, J. Anal. 12 (2004), 135-142. (2004) Zbl1097.47002MR2142970
  9. Meenakshi, A., On sums of EP matrices, Houston J. Math. 9 (1983), 63-69. (1983) Zbl0517.15006MR0699050
  10. Mitra, S. K., Bhimasankaram, P., Malik, S. B., Matrix Partial Orders, Shorted Operators and Applications, Series in Algebra 10 World Scientific, Hackensack (2010). (2010) Zbl1203.15023MR2647903
  11. Ramanathan, K., Sivakumar, K. C., 10.1007/s10957-007-9321-y, J. Optim. Theory Appl. 137 (2008), 99-104. (2008) Zbl1151.46055MR2386616DOI10.1007/s10957-007-9321-y

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