Balanced matrix: Difference between revisions

Revision as of 20:42, 18 March 2016

Revision as of 17:39, 1 July 2016

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\end{bmatrix}</math>

== 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''}|

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 &amp; Falkner 1988</ref> and therefore also balanced. Note that this condition is sufficient but not necessary for ''A'' to be balanced.

== Notes ==

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== References ==

* {{Citation

| last = Berge

| first = C.

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| publisher = Centre National de Recherche Scientifique

| ___location = Paris, France}}

* {{Citation

*{{Citation

| last1 = Ryan | first1 = D. M.

| last2 = Falkner | first2 = J. C.

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| volume = 35 | issue = 3 | pages = 442–456}}

{{DEFAULTSORT:Balanced Matrix}}

[[Category:Matrices]]