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. 
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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/

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