Null, column and row space

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>.