Dimensionality Assume there are k vectors What is their dimensionality? Vectors are linearly independent iff the linear combination only when The span of a set of vectors is the vector space generated by their linear combinations A basis of a vector space is a set of vectors that are linearly independent and that spans The cardinality of the basis of a vector space , i.e., the number of linearly independent vectors needed to span is called its dimensionality The bases (i.e., the basis vectors) may vary, but their cardinality remains the same