New results for EP matrices in indefinite inner product spaces

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• 作者：Ivana M. Radojevi? (1)
  
• 关键词：EP matrix ; indefinite matrix product ; reverse order law ; partial order ; indefinite inner product space ; 15A09 ; 06A06 ; 47B50
• 刊名：Czechoslovak Mathematical Journal
• 出版年：2014
• 出版时间：March 2014
• 年：2014
• 卷：64
• 期：1
• 页码：91-103
• 全文大小：149 KB
• 参考文献：1. / E. Arghiriade: Sur les matrices qui sont permutables avec leur inverse généralisée. Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. / 35 (1963), 244-51. (In French.)
  2. / A. Ben-Israel, T. N. E. Greville: Generalized Inverses. Theory and Applications. 2nd ed. CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC 15, Springer, New York, 2003.
  3. / D. S. Djordjevi?, V. Rako?evi?: Lectures on Generalized Inverses. University of Ni?, Faculty of Sciences and Mathematics, Ni?, 2008.
  4. / M. P. Drazin: Natural structures on semigroups with involution. Bull. Am. Math. Soc. / 84 (1978), 139-41.
  5. / I. Gohberg, P. Lancaster, L. Rodman: Indefinite Linear Algebra and Applications. Birkh?user, Basel, 2005.
  6. / R. E. Hartwig, I. J. Katz: On products of / EP matrices. Linear Algebra Appl. / 252 (1997), 339-45.
  7. / S. Jayaraman: EP matrices in indefinite inner product spaces. Funct. Anal. Approx. Comput. / 4 (2012), 23-1.
  8. / K. Kamaraj, K. Ramanathan, K. C. Sivakumar: Indefinite product of matrices and applications to indefinite inner product spaces. J. Anal. / 12 (2004), 135-42.
  9. / A. Meenakshi: On sums of EP matrices. Houston J. Math. / 9 (1983), 63-9.
  10. / S. K. Mitra, P. Bhimasankaram, S. B. Malik: Matrix Partial Orders, Shorted Operators and Applications. Series in Algebra 10, World Scientific, Hackensack, 2010.
  11. / K. Ramanathan, K. C. Sivakumar: Theorems of the alternative over indefinite inner product spaces. J. Optim. Theory Appl. / 137 (2008), 99-04.
  
• 作者单位：Ivana M. Radojevi? (1)
  
  1. Faculty of Sciences and Mathematics, Department of Mathematics, University of Ni?, Vi?egradska 33, 18000, Ni?, Serbia
  
• ISSN：1572-9141

文摘

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.