Scalar-Vector Multiplication

linear-algebra

Definition

Scalar-Vector Multiplication

Let $V$ be a vector space over a field $F$. Scalar-vector multiplication is the operation

$$\cdot :F\times V\to V,$$

under which

• the map $v\mapsto \lambda v$ is linear for each $\lambda \in F$,
• the map $\lambda \mapsto \lambda v$ is additive, and
• $1_F\cdot v=v$.