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{{Expert-subject|Mathematics|date=March 2011}}
In [[mathematics]], a '''balanced matrix''' ''B'' is a 0-1 matrix that does not contain any square submatrix of odd order having row and column sum equal to 2.
Balanced matrices are important in linear programs such as the [[set partitioning problem]], as they are naturally integer. 0-1 [[Totally unimodular]] matrices are a subset of balanced matrices, and balanced matrices are a subset of [[perfect matrix|perfect matrices]], 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 forbidden submatrix:
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