freeCodeCamp/guide/english/mathematics/linear-algebra/spans/index.md

17 lines
768 B
Markdown
Raw Blame History

This file contains ambiguous Unicode characters!

This file contains ambiguous Unicode characters that may be confused with others in your current locale. If your use case is intentional and legitimate, you can safely ignore this warning. Use the Escape button to highlight these characters.

---
title: Spans
---
## Spans
<!-- The article goes here, in GitHub-flavored Markdown. Feel free to add YouTube videos, images, and CodePen/JSBin embeds -->
##### Introduction
Let S be a nonempty subset of a vector space V. The span of S, denoted by span(S), is the set containing of all linear combinations of vectors in S. For convenience, we define span(∅)={0}.
or
Let S be a set of vectors in a vector space W. The subspace spanned by S is defined to be intersection W of all subspaces of V which contain S. When S is finite set of vectors, S={α1,α2,...,αn}, we shall simply call W the subspace spanned by the vectors α1,α2,...,αn.
#### More Information:
<!-- Please add any articles you think might be helpful to read before writing the article -->