Matrix equations over -symmetric and -skew symmetric matrices

✍ Scribed by Mehdi Dehghan; Masoud Hajarian

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 373 KB
• Volume: 59
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2010.03.052

✦ Synopsis

Let R ∈ C m×m and S ∈ C n×n be nontrivial involution matrices; i.e. R = R -1 = ±I and S = S -1 = ±I. An m × n 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

and

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.