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{{expert-subject|Mathematics}}
In [[mathematics]], a '''balanced matrix''' ''B'' is an [[integer matrix]] that does not contain any odd order 2-cycle submatricies (submatrix of order n where n is odd and the row and column sums equal 2).
Balanced matricies are important in linear programs such as the [[set partitioning problem]], 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.
The following matrix is a 3 order 2-cycle submatrix:
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0 & 1 & 1\\
\end{bmatrix}</math>
The following matrix is a balanced matrix as it does not contain the above nor any other odd order 2-cycle submatrix:
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| publisher = Centre National de Recherche Scientifique
| ___location = Paris, France}}
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