Definition:Affinely Dependent

Definition
Let $\R^n$ be the $n$-dimensional real Euclidean space.

Let $S = \set {x_1, \dots, x_r}$ be a finite subset of $\R^n$.

An element $x \in \R^n$ is affinely dependent on $S$ there exist real numbers $\set {\lambda_i: 1 \le i \le r}$ such that:
 * $(1): \quad x = \ds \sum_{i \mathop = 1}^r \lambda_i x_i$
 * $(2): \quad \ds \sum_{i \mathop = 1}^r \lambda_i = 1$

Also see

 * Definition:Affinely Independent