Let be the field of all complex numbers, the space of all matrices over , and the subspace of consisting of all symmetric matrices. The map satisfies that is -potent in implying that is -potent in , where then there exist an invertible matrix and with such that for every . Moreover, the inductive method used in this paper can be used to characterise similar maps from to .
"A Note on -Potence Preservers on Matrix Spaces over Complex Field." Abstr. Appl. Anal. 2013 (SI20) 1 - 8, 2013. https://doi.org/10.1155/2013/581683