Indicator vector

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 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

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