Span

==2024-12-11

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Theory

Let $V_n$ be a Vector Space over a field $\mathbb{F}$, and let $S$ be a non-empty Subset of $V_n$.

The span of S, denoted as span$(S)$, is the set of all possible Linear Combination of Vectors in $S$ and is defined as:

$$span(S)=\{c_1{v}_1+c_2{v}_2+\cdots +c_n{v}_n|v_i\in S,c_i\in \mathbb{F},n\in \mathbb{N}\}$$

where $c_i$ are scalars from the field $\mathbb{F}$, and $n$ is any no-negative integer.

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