Abstract
Some time in the early 2000's, I extended the routine CompanionMatrix in the LinearAlgebra package to compute what are called linearizations of what are called matrix polynomials. These are just univariate polynomials with matrix coefficients; isomorphically, these are matrices with univariate polynomial entries. Linearizations can be used to solve multivariate systems of equations by a number of techniques, which are `"well-known" in the sense that they are in books and papers. However well-known they are, they deserve to be better-known, and this expository paper gives some examples of some of the methods that can be used. Think of this as an extended help page for the code (which, if I am honest, is long overdue for an upgrade).
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