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New page: 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 forme...
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}\}.
==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}\}.