On relative residual bounds for the eigenvalues of a Hermitian matrix (Q1923214)

Let \(H\) denote a Hermitian matrix of order \(n\), let \(X\) denote an \(n \times m\) complex matrix with orthonormal rows, so that \(n\geq m\), and let \(M= X^*HX\). The author gives a bound for the relative distance between the eigenvalues of \(M\) and near eigenvalues of \(H\) in terms of the angle between the ranges of \(X\) and \(HX\).