Weighted acute perturbation for two matrices

Abstract EN

Using the method of generalized singular values decomposition, some results of the perturbation of the oblique projectors AA†MN and BB†MN are given, where A†MN is the weighted Moore–Penrose inverse of A, and M and N are two Hermitian positive definite matrices.

Also, an (M, N)-weighted acute perturbation for the two matrices A and B is introduced and the properties of this kind of perturbation are discussed.

Our work can be regarded as an extension of results on the orthogonal projectors AA† and BB† and the acute perturbation of the two matrices A and B.