Affine Combination

Last updated Nov 1, 2022

Let $V$ be a Vector Space over $\mathbb{R}$ and $x_{1}, \dots, x_{n} \in V$ for some $n \in \mathbb{N}$. Suppose $\lambda_{1}, \dots, \lambda_{n} \in \mathbb{R}$ and $\sum\limits_{i=1}^{n} \lambda_{i} = 1$. Then $$\lambda_{1} x_{1} + \cdots + \lambda_{n}x_{n}$$ is an Affine Combination of $x_{1}, \dots, x_{n}$.

• Real Numbers