A sin2Θ theorem for graded indefinite Hermitian matrices

This paper gives 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 . These theorems extend recent results on a definite Hermitian matrix in the graded form (Linear Algebra Appl. 311 (2000) 45) but the bounds here are more complicated in that they depend on not only relative gaps and norms of ΔA as in the definite case but also norms of some J-unitary matrices, where J is diagonal with ±1 on its diagonal. For two special but interesting cases, bounds on these J-unitary matrices are obtained to show that their norms are of moderate magnitude.