Geodesic
On matrices with pairwise orthogonal rows and columns
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIV, Tome 504 (2021), pp. 47-53
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We discuss possible forms of square matrices whose rows are pairwise orthogonal and the same is true of their columns. This discussion is applied to the problem of conditions under which a nonsingular binormal matrix is unitoid. A square matrix $A$ is said to be binormal if the matrices $AA^*$ and $A^*A$ commute. A square matrix is said to be unitoid if it can be brought to diagonal form by a (Hermitian) congruence. 
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     author = {Kh. D. Ikramov},
     title = {On matrices with pairwise orthogonal rows and columns},
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Kh. D. Ikramov. On matrices with pairwise orthogonal rows and columns. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIV, Tome 504 (2021), pp. 47-53. http://geodesic.mathdoc.fr/item/ZNSL_2021_504_a2/

[1] R. A. Horn, C. R. Johnson, Matrix Analysis, Second edition, Cambridge University Press, Cambridge, 2013 | Zbl