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 ∈ S such that x s = 1 if s ∈ T and x s = 0 if s ∉ T .

If S is countable and its elements are numbered so that S = { s 1 , s 2 , … , s n } , then x T = ( x 1 , x 2 , … , x n ) where x i = 1 if s i ∈ T and x i = 0 if s i ∉ 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.