The Depiction Of Maps Preserving Zeros Of A Polynomial

As a branch of the preserver problem, the exploration of linear maps preservingzeros of a polynomial is very meaningful. This is because that for differentpolynomials, mappings preserving commuting pairs, idempotent matrixes, zeroproducts and many others preserver problems are all included in it.Based on the introduction of the background and research status of the linearmaps preserving zeros of a polynomial, this thesis provides the general structure oflinear maps preserving zeros of the multilinear polynomial on matrix algebra. Themain work is as follows:(1) For polynomials with nonzero sums of coefficients, under certain technicalrestrictions we extend the number of the indeterminates from d <2nto anynumber d≥2and provide the general structure of linear maps preserving zeros ofthis kind of polynomials by the knowledge of group and special selected matrices.(2) For polynomials with vanishing sums of coefficients, under certaintechnical restrictions and special selected matrices, we provide the general structureof linear maps preserving zeros of this kind of polynomials on the basis of the proofthat linear maps preserve zeros of this kind of polynomials also preservingcommuting pairs.