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# 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 ( $\operatorname{null}(A)>0$).

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

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

Synonym:

non-invertible, singular transformation

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

65F35*no label found*15A12

*no label found*

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## Corrections

some changes in wording by rmilson ✓

size? by krissy ✓

Suggest link by archibal ✓

better definition by Mathprof ✓

size? by krissy ✓

Suggest link by archibal ✓

better definition by Mathprof ✓