singular

1 Singular

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 $n$.

Title singular Singular 2013-03-22 11:57:38 2013-03-22 11:57:38 Mathprof (13753) Mathprof (13753) 11 Mathprof (13753) Definition msc 65F35 msc 15A12 non-invertible singular transformation