If "V" is a vector space over the field "F", the general linear group of "V", written GL("V") or Aut("V"), is the group of all automorphisms of "V", i.e. the set of all bijective linear transformations , together with functional composition as group operation. If "V" has finite dimension "n", then GL("V") and are isomorphic. The isomorphism is not canonical; it depends on a choice of basis in "V". Given a basis of "V" and an automorphism "T" in GL("V"), we have then for every basis vector "e""i" that