singular
Singular
2001-11-12 02:30:40
2006-09-04 13:42:15
Definition
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\section{Singular}
An $ m \times n$ matrix $ A$ with entries from a field is called \emph{singular} if its rows or columns are linearly dependent. This is equivalent to the following conditions:
\begin{enumerate}
\item
The nullity of $ A$ is greater than zero ( $ \operatorname{null}(A) > 0$).
\item
The homogeneous linear system $ A\mathbf{x} = 0 $ has a non-trivial solution.
\end{enumerate}
If $m$ = $n$ this is equivalent to the following conditions:
\begin{enumerate}
\item
The determinant $ \det(A)=0$.
\item
The rank of $ A$ is less than $ n$.
\end{enumerate}