On Multilinear Polynomials In Four Variables Evaluated On Matrices

David Buzinski; Robin Winstanley

doi:10.1016/j.laa.2013.08.005

On Multilinear Polynomials In Four Variables Evaluated On Matrices

Rings and Algebras 2015-11-20 v1

Authors: 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 $0$ .

Keywords

positive polynomials polynomial theory hadamard matrices

Cite

@article{arxiv.1511.06331,
  title  = {On Multilinear Polynomials In Four Variables Evaluated On Matrices},
  author = {David Buzinski and Robin Winstanley},
  journal= {arXiv preprint arXiv:1511.06331},
  year   = {2015}
}

Comments

8 pages

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