The elliptic matrix completion problem (Q630533)

The author gives necessary and sufficient conditions on a nonnegative tensor to be diagonally equivalent to a tensor with prescribed slice sum. The following theorem is proved. Let \(H\) be a Hermitian matrix with partioned form \(H=\left[\begin{matrix} A & B\\ B^* & D\end{matrix}\right]\), where \(A\) has order \(r\). Order the eigenvalues of \(H\) and \(A\) so that \(\lambda_1(H)\geq \lambda_2(H)\geq\cdots\geq \lambda_n(H)\) and \(\lambda_1(A)\geq \lambda_2(A)\geq\cdots\geq \lambda_n(A)\). Then \(\lambda_i(H)\geq \lambda_i(A)\geq\lambda_{i+n-r}(H)\) for \(i= 1,2,\dots, r\).