Geodesic
General preservers of quasi-commutativity on Hermitian matrices
The electronic journal of linear algebra, Tome 17 (2008), pp. 436-444.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let H n be the set of all n $\times n$ hermitian matrices over C, n $\geq 3$. It is said that A, B $\in H$ n quasi-commute if there exists a nonzero $\xi \in C$ such that $AB = \xi $BA. Bijective not necessarily linear maps on hermitian matrices which preserve quasi-commutativity in both directions are classified.
Classification : 15A04, 15A27, 15A57
Keywords: general preserver, Hermitian matrices, quasi-commutativity 
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     title = {General preservers of quasi-commutativity on {Hermitian} matrices},
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Dolinar, Gregor; Kuzma, Bojan. General preservers of quasi-commutativity on Hermitian matrices. The electronic journal of linear algebra, Tome 17 (2008), pp. 436-444. http://geodesic.mathdoc.fr/item/ELA_2008__17__a14/