 The family is "linearly dependent" over "K" if there exists a non-empty "finite" subset "J" ⊆ "I" and a family {"a""j" | "j" ∈ "J"} of elements of "K", all non-zero, such that

A set "X" of elements of "V" is "linearly independent" if the corresponding family {"x"}"x"∈"X" is linearly independent.Equivalently, a family is dependent if a member is in the closure of the linear span of the rest of the family, i.e., a member is a linear combination of the rest of the family.The trivial case of the empty family must be regarded as linearly independent for theorems to apply.