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Line 2: {{expert-subject\|Mathematics}} In [[mathematics]], a '''balanced matrix''' ''B'' is an [[integer matrix]] that does not contain any odd order 2-cycle ~~submatricies~~submatrices (submatrix of order ''n'' where ''n'' is odd and the row and column sums equal 2). Balanced ~~matricies~~matrices are important in linear programs such as the [[set partitioning problem]], as they are naturally integer. [[Totally unimodular]] ~~matricies~~matrices are a subset of balanced ~~matricies~~matrices, and balanced ~~matricies~~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 submatrix:

Balanced matrix: Difference between revisions