The inverse eigenvalue problem of generalized reflexive matrices and its approximation (Q654624)

A matrix \(P\) is called a generalized reflection matrix if \(P^T=P\) and \(P^2=I\). For two given generalized reflection matrices \(P\) and \(Q\), a matrix \(A\) is called a generalized reflexive matrix with respect to (\(P,Q\)) if \(A=PAQ\). The authors consider the inverse eigenvalue problem for generalized reflexive matrices. Necessary and sufficient conditions for the solvability of the problem are derived and the solution formula is provided. Moreover, the authors study optimal approximations (in Frobenious norm) of a given matrix among the solutions to the above problem.