Balanced matrix: Difference between revisions

Revision as of 00:23, 29 October 2010

Revision as of 12:28, 27 March 2011

Line 1:

{{orphan|date=July 2010}}

{{expertExpert-subject|Mathematics|date=March 2011}}

In [[mathematics]], a '''balanced matrix''' ''B'' is an [[integer matrix]] that does not contain any odd order 2-cycle submatrices (submatrix of order ''n'' where ''n'' is odd and the row and column sums equal 2).

Line 22:

==Subsequence count==

An alternative method of identifying a balanced matrix that is also a zero-one matrix is through the subsequence count, where the subsequence count ''SC'' of any row s of matrix ''A'' is

:'''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''}|

Line 36:

| ___location = Paris, France}}

{{DEFAULTSORT:Balanced Matrix}}

[[Category:Matrices]]