Definition:Linearly Independent/Sequence/Real Vector Space

Definition
Let $\left({\R^n,+,\cdot}\right)_{\R}$ be a real vector space.

Let $\left \langle {\mathbf v_n} \right \rangle$ be a sequence of vectors in $\R^n$.

Then $\left \langle {\mathbf v_n } \right \rangle$ is linearly independent iff:


 * $\displaystyle \forall \left \langle {\lambda_n} \right \rangle \subseteq \R: \sum_{k \mathop = 1}^n \lambda_k \mathbf v_k = \mathbf 0 \implies \lambda_1 = \lambda_2 = \cdots = \lambda_n = 0$

where $\mathbf 0 \in \R^n$ is the zero vector and $0 \in \R$ is the zero scalar.

Also see

 * Linearly Dependent Sequence of Vector Space