linear span of a set of vectors

Topics

• linear algebra

The span of a set of vectors, also called linear span, is the linear space formed by all the vectors that can be written as linear combinations of the vectors belonging to the given set. Mathematically, a set of vectors $\{v_1,v_2\dots ,v_n\}\in \mathbb{V}$ is said to span $\mathbb{V}$ if for any $x\in \mathbb{V}$, there exists coefficients ${\beta }_1,{\beta }_2,\dots {\beta }_n\in \mathbb{R}$ such that:

$$x=\sum _{i=1}^n{\beta }_i{v}_i$$

In this case, $\mathbb{V}$ becomes the linear space containing all our spanned vectors.

Related