Geodesic
Congruence verification for involutive matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIII, Tome 496 (2020), pp. 87-93

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A finite computational process using only arithmetic operations is called a rational algorithm. Presently, no rational algorithm for checking the congruence of arbitrary complex matrices $A$ and $B$ is known. The situation may 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. In this publication, we propose a rational algorithm for checking the congruence of involutive matrices $A$ and $B$. 
@article{ZNSL_2020_496_a4,
     author = {Kh. D. Ikramov},
     title = {Congruence verification for involutive matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {87--93},
     publisher = {mathdoc},
     volume = {496},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_496_a4/}
}
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Kh. D. Ikramov. Congruence verification for involutive matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIII, Tome 496 (2020), pp. 87-93. http://geodesic.mathdoc.fr/item/ZNSL_2020_496_a4/