reserve X for set,
        n,m,k for Nat,
        K for Field,
        f for n-element real-valued FinSequence,
        M for Matrix of n,m,F_Real;

theorem Th64:
  for K be Field,
      V be finite-dimensional VectSp of K
  ex T be linear-transformation of V, (dim V) -VectSp_over K
    st T is bijective
  proof
    let K be Field;
    let V be finite-dimensional VectSp of K;
    set b = the OrdBasis of V;
    set W = (dim V) -VectSp_over K;
    set W0 = (dim V) -Group_over K;

    ex T be linear-transformation of V, (dim V) -VectSp_over K
    st T is bijective
     & for x be Element of V holds T.x= (x |-- b) by Th63;
    hence thesis;
  end;
