Absolute and relative perturbation bounds for invariant subspaces of matrices
This paper considers complex nonsingular \(n\times n\) matrices \(A\) and perturbed matrices \(A+E\) and derives absolute and relative bounds on the angle between a true and a perturbed invariant subspace, expressed in the Euclidean and the Frobenius norms, and containing \(\|E\|\) and an absolute separation, and \(\|A^{-1}E\|\) and a relative separation, respectively. With respect to relative bounds, no restrictions are placed on \(A\), on \(E\), or on the dimension of the subspaces. The bounds can be expressed in terms of subspace bases. For diagonalizable matrices the separations are expressed in terms of eigenvalues.
scientific article; zbMATH DE number 1443442