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 $n\times m$ 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.

Column space

The column space is the vector space formed by the span of the columns of the matrix $A$.

Row Space

The rows space is the vector space formed by the span of the rows of the matrix $A$.