Eigenvalues of centrosymmetric matrices (Q1195947)

Let \(V_ N\) be the set of \(N\)th order real centrosymmetric matrices such that \(V_ N=\{S\mid\) \(S=JSJ\}\) where \(J\) is the \(N\)th order counter identity matrix defined by \(J_{ij}=\delta_{i,N+1-j}\), \(i,j=1,2,\dots,N\). The paper considers the generalized eigenvalue problems \((S-\mu T)\{X\}=\{0\}\) and \((ST-\mu I)\{X\}=\{0\}\) with \(S,T\in V_ N\). A method is suggested to replace the eigenvalue problems by two equivalent smaller order eigenproblems. The method is effective in saving computing time.