In linear algebra, given a vector space V with a basis B of vectors indexed by an index set I (the cardinality of I is the dimensionality of V), its dual set is a set B of vectors in the dual space V with the same index set I such that B and B form a biorthogonal system. The dual set is always linearly independent but does not necessarily span V. If it does span V, then B is called the dual basis for the basis B.