#math/linear-algebra Suppose $S,T\in \mathcal{L}(V,W)$ and $\lambda \in F$. The **sum** $S+T$ is defined as $(S+T)(v)=Sv+Tv$ and **scalar product** $\lambda T$ is defined as $(\lambda T)(v)=\lambda(Tv)$. Additionally, if $T\in \mathcal{L}(U,V)\text{ and }S\in \mathcal{L}(V,W)$, then the **product** $ST\in \mathcal{L}(U,W)$ is defined by $(ST)(u)=S(Tu)$ for $u\in U$ (function compositions). From these alone, we can derive that linear maps, when the domain and range make sense, are **associative** $(T_{1}T_{2})T_{3}=T_{1}(T_{2}T_{3})$. We can also can derive that they are **distributive** $(S_{1}+S_{2})T=S_{1}T+S_{2}T$ and $S(T_{1}+T_{2})=ST_{1} +ST_{2}$