Abstract
We call a finite computational process using only arithmetic operations a rational algorithm. A rational algorithm that is able to check the congruence between arbitrary complex matrices A and B is currently not known. The situation may be different if A and B belong to a certain class of specialmatrices. For instance, there exist rational algorithms for the case where both matrices are Hermitian or unitary. In this paper, rational algorithms for checking the congruence between accretive or dissipative A and B are proposed.
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References
Kh. D. Ikramov, “Finite spectral procedures in linear algebra,” Programming (1), 56–69 (1994).
V. V. Prasolov, Polynomials (MTsNMO, Moscow, 2001) [in Russian].
R. A. Horn and V. V. Sergeichuk, “Canonical forms for unitary congruence and *congruence,” Linear Multilinear Algebra 57 (8), 777–815 (2009).
R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge Univ. Press, Cambridge, 2013).
R. A. Horn and V. V. Sergeichuk, “Canonical forms for complex matrices congruence and *congruence,” Linear Algebra Appl. 416 (2-3), 1010–1032 (2006).
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Original Russian Text © Kh. D. Ikramov, 2017, published in Matematicheskie Zametki, 2017, Vol. 101, No. 6, pp. 854–859.
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Ikramov, K.D. Checking the congruence between accretive matrices. Math Notes 101, 969–973 (2017). https://doi.org/10.1134/S0001434617050236
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DOI: https://doi.org/10.1134/S0001434617050236