An $m\times n$ matrix $A$ with entries from a field is called singular if its rows or columns are linearly dependent. This is equivalent to the following conditions:

1. 1.

   The nullity of $A$ is greater than zero ( $\operatorname{null}(A)>0$).

2. 2.

   The homogeneous linear system $A\mathbf{x}=0$ has a non-trivial solution.

If $m$ = $n$ this is equivalent to the following conditions:

1. 1.

   The determinant $\det(A)=0$.

2. 2.

   The rank of $A$ is less than $n$.