Inverse (Linear Map)

definitionvector-spaces

Definition

A linear map $T\in \mathcal{L}(V,W)$ is invertible if there exists a linear map $S\in \mathcal{L}(W,V)$ such that,

$$ST=I_v,\text{ and }TS=I_w.$$

In this case, we say that $S$ is an inverse of $T$.

Examples