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More restricting than the notion of balanced matrices is the notion of ''totally balanced'' matrices. A 0-1 matrix is called totally balanced if it does not contain a square submatrix having no repeated columns and all row sums and all column sums equal to 2. Equivalently, a matrix is totally balanced if and only if it does not contain a submatrix that is the incidence matrix of any cycle (no matter if of odd or even order). This characterization immediately implies that any totally balanced matrix is balanced. <ref>{{cite journal|doi=10.1137/0606070|title=Totally-balanced and Greedy Matrices|last1=Hoffman|first1=A.J.|last2=Kolen|first2=A.W.J.|last3=Sakarovitch|first3=M.|series=BW (Series)|year=1982|journal=SIAM. J. on Algebraic and Discrete Methods|pages=720–731}}</ref>
Moreover, any 0-1 matrix that is [[totally unimodular]] is also balanced. The following matrix is a balanced matrix as it does not contain any submatrix that is incidence matrix of an odd
:<math>\begin{bmatrix}
1 & 1 & 1 & 1\\
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