Geodesic
Pseudo-commutation classes of complex matrices and their decomplexification
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 26 (2023) no. 2, pp. 199-203 Cet article a éte moissonné depuis la source Math-Net.Ru

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The relation between complex matrices $H$ and $A$ given by the equality $HA=\overline{A}H$ is called the pseudo-commutation. The set $S_H$ of all $A$ that pseudo-commute with a nonsingular $n\times n$ matrix $H$ is called the pseudo-commutation class defined by $H$. Every class $S_H$ is a subspace of the space $M_n(\mathbf{C})$ interpreted as a real vector space of dimension $2n^2$. Under the assumption $\mathrm{dim}_{\mathbf{R}}S_H=n^2$, we find a necessary and sufficient condition for the possibility to decomplexify all the matrices in $S_H$ by one and the same similarity transformation. 
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     title = {Pseudo-commutation classes of complex matrices and their decomplexification},
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Kh. D. Ikramov. Pseudo-commutation classes of complex matrices and their decomplexification. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 26 (2023) no. 2, pp. 199-203. http://geodesic.mathdoc.fr/item/SJVM_2023_26_2_a5/

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