Definition:Linear Combination/Sequence

Definition
Let $G$ be an $R$-module.

Let $\left \langle {a_n} \right \rangle := \left \langle {a_j} \right \rangle_{1 \mathop \le j \mathop \le n}$ be a sequence of elements of $G$ of length $n$.

An element $b \in G$ is a linear combination of $\left \langle {a_n} \right \rangle$ :
 * $\displaystyle \exists \left \langle {\lambda_n} \right \rangle \subseteq R: b = \sum_{k \mathop = 1}^n \lambda_k a_k$

Also see

 * Definition:Linear Combination
 * Definition:Linear Combination of Subset
 * Definition:Linear Combination of Empty Set


 * Definition:Linear Span
 * Definition:Linear Transformation