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

2.
The homogeneous^{} linear system $A\mathbf{x}=0$ has a nontrivial solution.
If $m$ = $n$ this is equivalent to the following conditions:

1.
The determinant^{} $det(A)=0$.

2.
The rank of $A$ is less than $n$.
Title  singular 

Canonical name  Singular 
Date of creation  20130322 11:57:38 
Last modified on  20130322 11:57:38 
Owner  Mathprof (13753) 
Last modified by  Mathprof (13753) 
Numerical id  11 
Author  Mathprof (13753) 
Entry type  Definition 
Classification  msc 65F35 
Classification  msc 15A12 
Synonym  noninvertible 
Synonym  singular transformation 