A finite computational process using arithmetic operations only is called a rational algorithm. Presently, no rational algorithm for checking the congruence of arbitrary complex matrices A and B is known. The situation can be different if both 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. This paper proposes a rational algorithm for checking whether two involutive matrices A and B are congruent.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 496, 2020, pp. 87–93.
Translated by Kh. D. Ikramov.
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Ikramov, K.D. Checking the Congruence of Involutive Matrices. J Math Sci 255, 271–274 (2021). https://doi.org/10.1007/s10958-021-05368-5
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DOI: https://doi.org/10.1007/s10958-021-05368-5