Matrix equations over (R,S)-symmetric and (R,S)-skew symmetric matrices

  • Authors:

  • Mehdi Dehghan;Masoud Hajarian

  • Affiliations:

  • Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Avenue, Tehran 15914, Iran;Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Avenue, Tehran 15914, Iran

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2010

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Abstract

Let R@?C^m^x^m and S@?C^n^x^n be nontrivial involution matrices; i.e. R=R^-^1+/-I and S=S^-^1+/-I. An mxn complex matrix A is said to be a (R,S)-symmetric ((R,S)-skew symmetric) matrix if RAS=A (RAS=-A). The (R,S)-symmetric and (R,S)-skew symmetric matrices have many special properties and are widely used in engineering and scientific computations. In this paper, we consider the matrix equations A"1XB"1=C,A"1X=D"1,XB"2=D"2, and A"1X=D"1,XB"2=D"2,A"3X=D"3,XB"4=D"4, over the (R,S)-symmetric ((R,S)-skew symmetric) matrix X. We derive necessary and sufficient conditions for the existence of (R,S)-symmetric ((R,S)-skew symmetric) solutions for these matrix equations. Also we give the expressions for the (R,S)-symmetric ((R,S)-skew symmetric) solutions to the matrix equations.