An overview of relative \(\sin\Theta\) theorems for invariant subspaces of complex matrices
A complex square matrix is assumed to possess an invariant subspace, and a change of this subspace under a perturbation is measured by a certain ``pricipal'' angle. For its sinus, a number of estimates is reviewed/listed for both the additive and multiplicative perturbations and different assumptions about the matrix. The review, a successor of similar surveys, offers another set of explanations why certain high-accuracy diagonalization methods are so reliable. It is well written and well understandable, with both the ideas and technicalities amply illustrated by the three-dimensional or partitioned examples.
scientific article; zbMATH DE number 1546544