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 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.

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.

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