Difference between revisions of "Span"
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:<math>Span\{\boldsymbol{x}_{1},\boldsymbol{x}_{2},\dots,\boldsymbol{x}_{n}\}:=\{\boldsymbol{v}\in\mathbb{R}^{n}|\boldsymbol{v}=a_{1}\boldsymbol{x}_{1}+a_{1}\boldsymbol{x}_{1}+\dots+a_{n}\boldsymbol{x}_{n},\; \forall a_{i}\in\mathbb{R}\}. | :<math>Span\{\boldsymbol{x}_{1},\boldsymbol{x}_{2},\dots,\boldsymbol{x}_{n}\}:=\{\boldsymbol{v}\in\mathbb{R}^{n}|\boldsymbol{v}=a_{1}\boldsymbol{x}_{1}+a_{1}\boldsymbol{x}_{1}+\dots+a_{n}\boldsymbol{x}_{n},\; \forall a_{i}\in\mathbb{R}\}. | ||
</math> | </math> | ||
| − | [[Category: | + | [[Category:Linear algebra]] |
| − | [[Category: | + | [[Category:Mathematics]] |
Revision as of 19:34, July 13, 2016
In mathematics Span has many concepts.
Vector span
The span of a list of vectors <math>\{\boldsymbol{x}_{1},\boldsymbol{x}_{2},\dots,\boldsymbol{x}_{n}\}</math> is the space formed by all linear combinations of the vectors,
- <math>Span\{\boldsymbol{x}_{1},\boldsymbol{x}_{2},\dots,\boldsymbol{x}_{n}\}:=\{\boldsymbol{v}\in\mathbb{R}^{n}|\boldsymbol{v}=a_{1}\boldsymbol{x}_{1}+a_{1}\boldsymbol{x}_{1}+\dots+a_{n}\boldsymbol{x}_{n},\; \forall a_{i}\in\mathbb{R}\}.
</math>