Null, column and row space

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 $n\times m$ matrix $A$ is as,

$\{{\boldsymbol {x}}\in \mathbb {R} ^{m}|A{\boldsymbol {x}}={\boldsymbol {0}}\}$\; .

The null space is all so known as the solution space.