An n × n complex matrix A is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix P if A = PAP (A = — PAP). The reflexive and anti-reflexive matrices have ...

A comprehensive theory of the matrix linear equation AX + XB = C is presented. The equation is viewed as a vector equation LX = C in the vector space of all m × n matrices. As the main result, two ...