Geodesic
Binormal matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXX, Tome 463 (2017), pp. 132-141

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A square complex matrix $A$ is said to be binormal if the associated matrices $A^*A$ and $AA^*$ commute. This matrix class yields a meaningful finite-dimensional extension for the concept of normality. The paper can be regarded as a survey of the properties of binormal matrices. 
@article{ZNSL_2017_463_a9,
     author = {Kh. D. Ikramov},
     title = {Binormal matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {132--141},
     publisher = {mathdoc},
     volume = {463},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_463_a9/}
}
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Kh. D. Ikramov. Binormal matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXX, Tome 463 (2017), pp. 132-141. http://geodesic.mathdoc.fr/item/ZNSL_2017_463_a9/