Geodesic
Rationally verifiable necessary conditions for Hermitian congruence of complex matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 120-128 
Kh. D. Ikramov. Rationally verifiable necessary conditions for Hermitian congruence of complex matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 120-128. http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a7/
@article{ZNSL_2019_482_a7,
     author = {Kh. D. Ikramov},
     title = {Rationally verifiable necessary conditions for {Hermitian} congruence of complex matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {120--128},
     year = {2019},
     volume = {482},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a7/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A finite computational process using arithmetic operations only is called a rational algorithm. Matrices $A$ and $F$ are said to be Hermitian congruent if $F = Q^*AQ$ for a nonsingular matrix $Q$. The paper gives a survey of necessary conditions for Hermitian congruence verifiable by rational algorithms.

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