 A vector space can be of finite-dimension or infinite-dimension depending on the number of linearly independent basis vectors.The definition of linear dependence and the ability to determine whether a subset of vectors in a vector space is linearly dependent are central to determining a basis for a vector space.A sequence of vectors formula_1 from a vector space "V" is said to be "linearly dependent", if there exist scalars formula_2 , not all zero, such that
where formula_4 denotes the zero vector.