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If a 0-1 matrix ''A'' has SC(''s'') ≤ 1 for all rows ''s'' = 1, ..., ''m'', then ''A'' has a unique subsequence, is totally unimodular<ref name="RyanFalkner" /> and therefore also balanced. Note that this condition is sufficient but not necessary for ''A'' to be balanced. In other words, the 0-1 matrices with SC(''s'') ≤ 1 for all rows ''s'' = 1, ..., ''m'' are a proper subset of the set of balanced matrices.
As a more general notion, a matrix where every entry is either 0, 1 or -1 is called balanced if in every submatrix with two nonzero entries per row and column, the sum of the entries is a multiple of 4.<ref>{{citation|doi=10.1016/j.disc.2005.12.033|title=Balanced matrices|journal=Discrete Mathematics|volume=306|issue=19–20|pages=2411|year=2006|last1=Conforti|first1=Michele|last2=Cornuéjols|first2=Gérard|last3=Vušković|first3=Kristina|author3-link= Kristina Vušković |url=http://eprints.whiterose.ac.uk/74351/2/surveyFINAL.pdf}} A retrospective and tutorial.</ref>
== References ==
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