Algebra on the Set of Linear Maps

definitionvector-spaces

Definition

If $S,T\in \mathcal{L}(V,W)$ and $\lambda \in \mathbb{F}$, define,

1. $(S+T)(v)=Sv+Tv$.
2. $(\lambda T)(v)=\lambda (Tv)$. Which are an addition and scalar multiplication on $\mathcal{L}(V,W)$.

Theorem

$\mathcal{L}(V,W)$ is a vector space over $\mathbb{F}$.

Examples