A \(\sin 2\varTheta\) theorem for graded indefinite Hermitian matrices
The study concerns the double angle theorems that bound the change in an invariant subspace of an indefinite Hermitian matrix in the graded form \(H=D^*AD\) subject to a perturbation \(H\to\widetilde H=D^* (A+\Delta A)D\). These theorems extend a \(\sin 2\theta\) theorem for positive definite Hermitian matrices [Linear Algebra Appl. 311, 45-60 (2000; Zbl 0963.15017)] to indefinite graded Hermitian matrices. The bounds here are more complicated since they depend also on norms of some \(J\)-unitary matrices. Bounds on these \(J\)-unitary matrices are computed.
scientific article; zbMATH DE number 1886841