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arXiv · 1403.5454

Functional identities on matrix algebras

Matej Brešar·Špela Špenko
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Abstract

Complete solutions of functional identities $\sum_{k\in K}F_k(\bar{x}_m^k)x_k = \sum_{l\in L}x_lG_l(\bar{x}_m^l)$ on the matrix algebra $M_n(\mathbb{F})$ are given. The nonstandard parts of these solutions turn out to follow from the Cayley-Hamilton identity.

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Matej Brešar, Špela Špenko. 2014-11-09. Functional identities on matrix algebras. https://arxiv.org/abs/1403.5454

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