Maps preserving zeros of a polynomial

Preserving zeros of a polynomial

We study non-linear surjective mappings on subsets of Mn(F), which preserve the zeros of some fixed polynomials in noncommuting variables. Mathematics subject classification (2000): 15A99, 16W99.

A Survey of Invertibility and Spectrum Preserving Linear Maps

Banach-stone Theorems for Maps Preserving Common Zeros

Let X and Y be completely regular spaces and E and F be Hausdorff topological vector spaces. We call a linear map T from a subspace of C(X, E) into C(Y, F ) a Banach-Stone map if it has the form Tf(y) = Sy(f(h(y)) for a family of linear operators Sy : E → F , y ∈ Y , and a function h : Y → X. In this paper, we consider maps having the property: (Z) ∩ki=1 Z(fi) 6= ∅ ⇐⇒ ∩ k i=1Z(Tfi) 6= ∅, where ...

Linear maps preserving or strongly preserving majorization on matrices

For $A,Bin M_{nm},$ we say that $A$ is left matrix majorized (resp. left matrix submajorized) by $B$ and write $Aprec_{ell}B$ (resp. $Aprec_{ell s}B$), if $A=RB$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $R.$ Moreover, we define the relation $sim_{ell s} $ on $M_{nm}$ as follows: $Asim_{ell s} B$ if $Aprec_{ell s} Bprec_{ell s} A.$ This paper characterizes all linear p...

Computing a Perturbation Bound for Preserving the Number of Common Zeros of a Polynomial System

We propose a method for computing a perturbation bound that preserves the number of common zeros in (C×)n of a polynomial system (f1, . . . , fn), where C× = C \ {0} and fj ∈ C[x1, . . . , xn], by using Stetter’s results on the nearest polynomial with a given zero, Bernshtein’s theorem, and minimization techniques for rational functions such as sum of squares (SOS) relaxations.