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Cybernetics And Systems Analysis
International Theoretical Science Journal
UDC 512.61
N.A. Vareniuk1, N.I. Tukalevska2


1 V.M. Glushkov Institute of Cybernetics, National Academy
of Sciences of Ukraine, Kyiv, Ukraine

nvareniuk@ukr.net

2 V.M. Glushkov Institute of Cybernetics, National Academy
of Sciences of Ukraine, Kyiv, Ukraine

EXISTENCE AND UNIQUENESS OF WEIGHTED PSEUDOINVERSE
MATRICES WITH NONSINGULAR INDEFINITE WEIGHTS

Abstract. For arbitrary complex matrices, necessary and sufficient conditions for the existence and uniqueness of weighted pseudoinverses with nonsingular indefinite weights are obtained. The representations of these matrices are obtained in terms of the coefficients of characteristic polynomials of the Hermitizable matrices.

Keywords: weighted pseudoinverse matrices with indefinite weights, Hermitizable matrix.



FULL TEXT

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