Abstract
By using the method of generalized singular values decomposition, we establish a canonical theorem for a pair of oblique projectors AA MN † and BB MN † , give some new results for perturbations of AA MN † and BB MN † , where A MN † 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 † and BB † . Some numerical examples are given to illustrate the results.
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