Perturbation for a pair of oblique projectors AAMN† and BBMN†

By using the method of generalized singular values decomposition, we establish a canonical theorem for a pair of oblique projectors AAMN† and BBMN†, give some new results for perturbations of AAMN† and BBMN†, where AMN† is the weighted Moore–Penrose inverse of matrix A, M and N are two Hermitian positive definite matrices and B is a matrix obtained from a perturbation of A  . Our work can be seen as the extended results for orthogonal projectors AA†AA† and BB†BB†. Some numerical examples are given to illustrate the results.