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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 := s ∈ S {\displaystyle x_{T}:=_{s\in S}} such that x s = 1 {\displaystyle x_{s}=1} if s ∈ T {\displaystyle s\in T} and x s = 0 {\displaystyle x_{s}=0} if s ∉ T . {\displaystyle s\notin T.}
If S is countable and its elements are numbered so that S = { s 1 , s 2 , … , s n } {\displaystyle S=\{s_{1},s_{2},\ldots ,s_{n}\}} , then x T = {\displaystyle x_{T}=} where x i = 1 {\displaystyle x_{i}=1} if s i ∈ T {\displaystyle s_{i}\in T} and x i = 0 {\displaystyle x_{i}=0} if s i ∉ T . {\displaystyle 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.
An indicator vector is a special case of an indicator function.