Affine independence (incomplete)

Dependencies:

1. Vector Space
2. Linear independence

$\newcommand{\defeq}{=}$ Let $X \defeq \{x^{(1)}, \ldots, x^{(n)}\}$ be vectors over field $F$. $X$ is affinely independent iff (the following conditions are equivalent):

1. $\forall \alpha \in F^n$, if $\sum_{i=1}^n \alpha_i = 0$ and $\sum_{i=1}^n \alpha_ix^{(i)} = 0$, then $\alpha = 0$.
2. $\{x^{(1)}-x^{(n)}, \ldots, x^{(n-1)} - x^{(n)}\}$ is linearly independent.

Proof of equivalence (incomplete)

Dependency for:

1. Dimension of a polyhedron
2. Dimension of a set of vectors

Info:

• Depth: 5
• Number of transitive dependencies: 5

Transitive dependencies:

1. Group
2. Ring
3. Field
4. Vector Space
5. Linear independence