Dimensionality

Abstract

Let X be a vector space and let S be a subset of it. We say S is linearly independent if for every finite subset {x₁,…, x _n } of S, the equation

$${a_1}{x_1} + \cdots + {a_n}{x_n} = 0$$

((2.1))

holds if and only if a₁ = a₂ = ⋯ = a_n = 0. A (finite) sum like the one in (2.1) is called a linear combination of x₁,…, x_n.