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 $A𝐱=0$ has a non-trivial 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	2013-03-22 11:57:38
Last modified on	2013-03-22 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	non-invertible
Synonym	singular transformation