On the J-singular values of a matrix (Q1096696)

Let \(E_ n\) be the unit matrix and \(J=\left[ \begin{matrix} 0\\ -E_ n\end{matrix} \begin{matrix} E_ n\\ 0\end{matrix} \right]\). The eigenvalues of the matrix \(C=JA^ TJA\) are called the J-singular values of the real 2n\(\times 2n\) matrix A. The author proves that the J-singular values of real 2n\(\times 2n\) matrices are invariant with respect to products by symplectic matrices.