Polynomially Isometric Matrices in Low Dimensions

Abstract

Given two $d\times d$ matrices, say $A$ and $B$, when do $p(A)$ and $p(B)$ have the same ``size'' for every polynomial $p$? In this article, we provide definitive results in the cases $d=2$ and $d=3$ when the notion of size used is the spectral norm.

To appear in The American Mathematical Monthly