Matrix inverse problem and its optimal approximation problem for \(R\)-symmetric matrices (Q2381343)

Let \(R\) be a nontrivial involution. A matrix \(A\) is called \(R\)-symmetric if \(RAR= A\). This paper focus on the following matrix inverse problem: Given matrices \(Z\) and \(B\), find an \(R\)-symmetric matrix \(A\) such that \(AZ= B\). The solvability is analysed and expressions of the solution with \(R\) being Hermitian are derived. When the problem is inconsistent, then the least squares solution is considered.