Abstract
A finite computational process using arithmetic operations only is called a rational algorithm. Presently, no rational algorithm is available that is able to check the congruence of arbitrary complex matrices A and B. In this paper, we propose a rational algorithm of verification that works under less stringent conditions than all the conditions known by now.
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REFERENCES
Kh. D. Ikramov, ‘‘On finite spectral procedures in linear algebra,’’ Program., No. 1, 56–69 (1994).
R. A. Horn and Ch. R. Johnson, Matrix Analysis, 2nd ed. (Cambridge Univ. Press, Cambridge, 2013).
Kh. D. Ikramov, ‘‘On the congruent selection of Jordan blocks from a singular square matrix,’’ Numer. Anal. Appl. 11 (3), 204–207 (2018).
M. G. Krein and M. A. Naimark, ‘‘The method of symmetric and Hermitian forms in the theory of the separation of the roots of algebraic equations,’’ Linear Multilinear Algebra 10 (4), 265–308 (1981).
Kh. D. Ikramov, Numerical Solution of Matrix Equations (Nauka, Moscow, 1984) [in Russian].
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Translated by Kh. Ikramov
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Ikramov, K.D., Usov, V.A. An Algorithm Verifying the Congruence of Complex Matrices Whose Cosquares Have Eigenvalues of Modulus One. MoscowUniv.Comput.Math.Cybern. 44, 176–184 (2020). https://doi.org/10.3103/S0278641920040020
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DOI: https://doi.org/10.3103/S0278641920040020