Difference between revisions of "Null, column and row 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:Linear | + | [[Category:Linear Algebra]] |
Latest revision as of 14:35, July 28, 2016
In mathematics a matrix can be categorised by its null, column and to a lesser extent its column space. These are all vector spaces associated 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>.