Linear Combination

Last updated Nov 1, 2022

Let $V$ be a Vector Space on Field $F$ and let $\mathbf{x}{1}, \dots \mathbf{x}{n} \in V$ for some $n \in \mathbb{Z}{\geq 0}$. Suppose $c{1}, \dots, c_{n} \in F$. Then $$c_{1} \mathbf{x}{1} + \cdots + c{n} \mathbf{x}n$$ is a Linear Combination of $\mathbf{x}{1}, \dots \mathbf{x}_{n}$.

1. If $n = 0$, the null Linear Combination is taken to be $\mathbf{0}$.