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In [[mathematics]], a '''balanced matrix''' ''B'' is
The following matrix is an odd order 2-cycle submatrix:
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\end{bmatrix}.</math>
The following matrix is a balanced matrix as it does not contain A nor any other odd order 2-cycle submatrix:
Balanced matricies are important in linear programs as they are naturally integer. [[Totally unimodular]] matricies are a subset of balanced matricies, and balanced matricies are a subset of perfect matricies.▼
:<math>B=\begin{bmatrix}
1 & 1 & 1 & 1\\
1 & 1 & 0 & 0\\
1 & 0 & 1 & 0\\
1 & 0 & 0 & 1\\
\end{bmatrix}.</math>
▲Balanced matricies are important in linear programs as they are naturally integer. [[Totally unimodular]] matricies are a subset of balanced matricies, and balanced matricies are a subset of perfect matricies, therefore any matrix that is totally unimodular is also balanced, however a balanced matrix may not necessarily be totally unimodular.
== References ==
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