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Square Roots of Hermitian Matrices and a Rational Algorithm for Checking Their Congruence

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Abstract

A finite computational process using only arithmetical operations is called a rational algorithm. Presently, there is no known rational algorithm for checking congruence between arbitrary complex matrices A and B. The situation may be different if A and B belong to a special matrix class. For instance, there exist rational algorithms for the cases where both matrices are Hermitian, unitary, or accretive. In this publication, we propose a rational algorithm for checking congruence between matrices A and B that are square roots of Hermitian matrices.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia

    Kh. D. Ikramov

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  1. Kh. D. Ikramov
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Correspondence to Kh. D. Ikramov.

Additional information

Russian Text © The Author(s), 2019, published in Vestnik Moskovskogo Universiteta, Seriya 15: Vychislitel’naya Matematika i Kibernetika, 2019, No. 3, pp. 11–16.

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Ikramov, K.D. Square Roots of Hermitian Matrices and a Rational Algorithm for Checking Their Congruence. MoscowUniv.Comput.Math.Cybern. 43, 95–100 (2019). https://doi.org/10.3103/S0278641919030026

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  • DOI: https://doi.org/10.3103/S0278641919030026

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