Definition:Linear Combination/Sequence

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

Let $\sequence {a_n} := \sequence {a_j}_{1 \mathop \le j \mathop \le n}$ be a sequence of elements of $M$ of length $n$.

An element $b \in M$ is a linear combination of $\sequence {a_n}$ :
 * $\ds \exists \sequence {\lambda_n} \subseteq R: b = \sum_{k \mathop = 1}^n \lambda_k a_k$

Also see

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


 * Definition:Linear Span
 * Definition:Linear Transformation