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 ∈ S {\displaystyle x_{T}:=(x_{s})_{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 = ( x 1 , x 2 , … , x n ) {\displaystyle x_{T}=(x_{1},x_{2},\ldots ,x_{n})} 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 (countable) case of an indicator function.