Scalar multiplication is the process of multiplying a scalar to an element in a set.

## constituents

- A set \(V\)
- Some \(\lambda \in \mathbb{F}\)
- Each \(v \in V\)

## requirements

scalar multiplication is defined by a function that results in \(\lambda v \in V\) (maps back to the space!) to each \(\lambda \in \mathbb{F}\) and each \(v \in V\).