Category:Definitions/Linear Combinations

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This category contains definitions related to Linear Combinations.
Related results can be found in Category:Linear Combinations.


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 $\sequence {a_n}$ if and only if:

$\ds \exists \sequence {\lambda_n} \subseteq R: b = \sum_{k \mathop = 1}^n \lambda_k a_k$

Subcategories

This category has the following 2 subcategories, out of 2 total.