The reflexive and anti-reflexive solutions of the matrix equation AX=B

✍ Scribed by Zhen-yun Peng; Xi-yan Hu

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 177 KB
• Volume: 375
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(03)00607-4

✦ Synopsis

An n × n complex matrix P is said to be a generalized reflection matrix if P H = P and P 2 = I . An n × n complex matrix A is said to be a reflexive (or anti-reflexive) matrix with respect to the generalized reflection matrix P if A = P AP (or A = -P AP ). This paper establishes the necessary and sufficient conditions for the existence of and the expressions for the reflexive and anti-reflexive with respect to a generalized reflection matrix P solutions of the matrix equation AX = B. In addition, in corresponding solution set of the equation, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm have been provided.