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arXiv · 1511.06331

On Multilinear Polynomials In Four Variables Evaluated On Matrices

David Buzinski·Robin Winstanley
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Abstract

Let $K$ be an algebraically closed field of characteristic $0$ and let $M_n(K)$, $n \ge 3$, be the matrix ring over $K$. We will show that the image of any multilinear polynomial in four variables evaluated on $M_n(K)$ contains all matrices of trace $0$.

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David Buzinski, Robin Winstanley. 2015-11-19. On Multilinear Polynomials In Four Variables Evaluated On Matrices. https://doi.org/10.1016/j.laa.2013.08.005

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