indicator vector

In mathematics, the indicator vector, characteristic vector, or incidence vector of a subset T of a set S is the vector $x\_T\; :=\; (x\_s)\_\{s\backslash in\; S\}$ such that $x\_s\; =\; 1$ if $s\; \backslash in\; T$ and $x\_s\; =\; 0$ if $s\; \backslash notin\; T.$

If S is countable and its elements are numbered so that $S\; =\; \backslash \{s\_1,s\_2,\backslash ldots,s\_n\backslash \}$, then $x\_T\; =\; (x\_1,x\_2,\backslash ldots,x\_n)$ where $x\_i\; =\; 1$ if $s\_i\; \backslash in\; T$ and $x\_i\; =\; 0$ if $s\_i\; \backslash notin\; T.$

To put it more simply, the indicator vector of T is a vector with one element for each element in S, with that element being one if the corresponding element of S is in T, and zero if it is not.{{cite book|title=Mathematical Classification and Clustering|first= Boris Grigorʹevich |last=Mirkin|page=112|isbn=0-7923-4159-7|year=1996|publisher= Springer |url=https://books.google.com/books?id=brzLe4X4ypEC&dq=indicator+vector+subset&pg=PA170|access-date=10 February 2014}}{{cite journal|title=A Tutorial on Spectral Clustering|first=Ulrike|last=von Luxburg|author-link= Ulrike von Luxburg |journal=Statistics and Computing|volume=17|issue=4|year=2007|page=2|url=http://www.kyb.mpg.de/fileadmin/user_upload/files/publications/attachments/Luxburg07_tutorial_4488%5B0%5D.pdf|access-date=10 February 2014|archive-url=https://web.archive.org/web/20110206100855/http://www.kyb.mpg.de/fileadmin/user_upload/files/publications/attachments/Luxburg07_tutorial_4488%5B0%5D.pdf#91;0].pdf|archive-date=6 February 2011|url-status=dead}}{{cite book|title=Decoding Linear Codes Via Optimization and Graph-based Techniques|first=Mohammad H. |last=Taghavi|page=21|year=2008|isbn=9780549809043 |url=https://books.google.com/books?id=6UCpDYih3WcC&dq=%22indicator+vector%22+subset&pg=PA21|access-date=10 February 2014}}

An indicator vector is a special (countable) case of an indicator function.