Modules I

Abstract

Let V be a vector space over a field F, and let τ ∈ L(V). Then for any polynomial p(x) ∈ F[x], the operator p(τ) is well-defined. For instance, if p(x) = 1 + 2x + x³, then

$$p\left( \tau \right) = l + 2\tau + {\tau ^3}$$

where ι is the identity operator, and τ ³ is the threefold composition τ o τ o τ.