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

If S is countable and its elements are numbered so that $$S = \{s_1,s_2,\ldots,s_n\}$$, then $$x_T = (x_1,x_2,\ldots,x_n)$$ where $$\(x_i = 1 if s_i \in T and x_i = 0$$ if $$s_i \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.[1][2][3]

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

Notes

Mirkin, Boris Grigorʹevich (1996). Mathematical Classification and Clustering. p. 112. ISBN 0-7923-4159-7. Retrieved 10 February 2014.
von Luxburg, Ulrike (2007). "A Tutorial on Spectral Clustering" (PDF). Statistics and Computing 17 (4): 2. Retrieved 10 February 2014.
Decoding Linear Codes Via Optimization and Graph-based Techniques. ProQuest. 2008. p. 21. Retrieved 10 February 2014. |first1= missing |last1= in Authors list (help)

Mathematics Encyclopedia