Balanced matrix: Difference between revisions

Revision as of 12:56, 8 August 2012

Revision as of 12:59, 8 August 2012

Line 25:

:'''SC''' = |{''t'' | [''a''_''sj''&nbsp;=&nbsp;1, ''a''_''ij''&nbsp;=&nbsp;0 for ''s''&nbsp;<&nbsp;''i''&nbsp;<&nbsp;''t'', ''a''_''tj''&nbsp;=&nbsp;1], ''j''&nbsp;=&nbsp;1,&nbsp;...,&nbsp;''n''}|

If a matrix ''A'' has SC(''s'')&nbsp;≤&nbsp;1 for all rows ''s''&nbsp;=&nbsp;1,&nbsp;...,&nbsp;''m'', then ''A'' has a unique subsequence, is totally unimodular<ref>Ryan 1988</ref> and therefore also balanced. Note that this condition is sufficient but not necessary for ''A'' to be balanced.

== References ==