A finite algorithm that uses arithmetic operations only is said to be rational. There exist rational methods for checking the congruence of a pair of Hermitian matrices or a pair of unitary ones. We propose a rational algorithm for checking the congruence of general normal matrices.
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Dedicated to the blessed memory of A.A. Abramov
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Ikramov, K.D., Nazari, A.M. A Heuristic Rational Algorithm for Checking the Congruence of Normal Matrices. Comput. Math. and Math. Phys. 60, 1601–1608 (2020). https://doi.org/10.1134/S0965542520100097
- Toeplitz decomposition
- indices of inertia
- Pythagorean triples