Weighted pseudoinversion with indefinite weights

Abstract

We present the definition of weighted pseudoinverse matrices with nonsingular indefinite weights and study these matrices. The theorems on existence and uniqueness for these matrices are proved. Weighted pseudoinverse matrices with indefinite weights are represented in terms of the coefficients of characteristic polynomials of symmetrizable matrices. The decompositions of weighted pseudoinverse matrices into matrix power series and products and their limit representations are obtained. We also propose regularized iterative methods for the determination of these matrices.