Null space

The null space (also spelt nullspace) of a m by n matrix A is the set of all vectors v which are solutions to the equation:

Av = 0

This is the same as the kernel of A if it is interpreted as a linear map.

In set notation, Nul A = {v: v is in Rⁿ and Av = 0 }

The nullity of a matrix is the dimension of its null space. The rank of any matrix plus its nullity equals the number of columns of that matrix.