Geodesic
Congruence criteria for normal and conjugate-normal matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 129-134

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Complex $n\times n$ matrices $A$ and $B$ are said to be $T$-congruent if $B = S^T AS$ and $*$-congruent if $B = S^* AS$, where $S$ is an arbitrary nonsingular matrix. For several facts related to normal matrices and $*$-congruences, analogs in the theory of $T$-congruences, concerning conjugate-normal matrices, are found. 
@article{ZNSL_2019_482_a8,
     author = {Kh. D. Ikramov},
     title = {Congruence criteria for normal and conjugate-normal matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {129--134},
     publisher = {mathdoc},
     volume = {482},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a8/}
}
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Kh. D. Ikramov. Congruence criteria for normal and conjugate-normal matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 129-134. http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a8/