Unifying Perturbation Bounds for Invariant Subspaces
I. Ipsen
Department of Mathematics
North Carolina State University
Raleigh, NC, USA
Abstract: We present absolute and relative perturbation bounds for angles between invariant subspaces of complex square matrices, in the two-norm and in the Frobenius norm. The bounds are extensions of Davis and Kahan's sin(theta) theorems to general matrices and invariant subspaces of any dimension.
Our goal is to unify absolute and relative bounds. To this end we will establish a general bound for invariant subspaces that implies both, absolute and relative bounds, as well as new bounds.