basis

definition

• a set of vectors in V form a basis for V if
  • each vector in the set are linearly independent of each other
  • they span the vector space (meaning each vector in the space can be expressed as linear combination of the basis vectors)
  • 

example

• given subspace S. basis of S is set B that has
  • minimum cardinality
  • span(B) = S
• cardinality of B is the dimension of S