Difference between revisions of "Null, column and row space"
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| − | In mathematics a [[matrix]] can be catergorised by its null, column and to a lesser extent its column space. These are all [[vector]] | + | In mathematics a [[matrix]] can be catergorised by its null, column and to a lesser extent its column space. These are all [[vector space]]s asscoiated with a particular matrix. |
==Null space== | ==Null space== | ||
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The rows space is the vector space formed by the [[span]] of the rows of the matrix <math>A</math>. | The rows space is the vector space formed by the [[span]] of the rows of the matrix <math>A</math>. | ||
| − | [[Category: | + | [[Category:Linear algebra]] |
Revision as of 21:28, June 8, 2008
In mathematics a matrix can be catergorised by its null, column and to a lesser extent its column space. These are all vector spaces asscoiated with a particular matrix.
Null space
The null space of a <math>n\times m</math> matrix <math>A</math> is as,
- <math>\{\boldsymbol{x}\in\mathbb{R}^m|A\boldsymbol{x}=\boldsymbol{0}\}</math>.
The null space is all so known as the solution space.
Column space
The column space is the vector space formed by the span of the columns of the matrix <math>A</math>.
Row Space
The rows space is the vector space formed by the span of the rows of the matrix <math>A</math>.