The images of multilinear polynomials evaluated on $3\times 3$ matrices
The images of multilinear polynomials evaluated on $3\times 3$ matrices
Let $p$ be a multilinear polynomial in several noncommuting variables, with coefficients in an algebraically closed field $K$ of arbitrary characteristic. In this paper we classify the possible images of $p$ evaluated on $3\times 3$ matrices. The image is one of the following: {0}, the set of scalar matrices, a …