Geodesic
An attempt of spectral theory for the $*$-congruence transformations
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 114-119

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The paper discusses the possibility of reducing a square complex matrix $A$ to a direct sum of smaller matrices by using $*$-congruence transformations. It turns out that this possibility is related to appropriate partitions of the spectrum of the cosquare of $A$. This makes it possible to associate the direct summands of the sum with subsets of the latter spectrum. 
@article{ZNSL_2019_482_a6,
     author = {Kh. D. Ikramov},
     title = {An attempt of spectral theory for the $*$-congruence transformations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {114--119},
     publisher = {mathdoc},
     volume = {482},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a6/}
}
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Kh. D. Ikramov. An attempt of spectral theory for the $*$-congruence transformations. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 114-119. http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a6/