frame a b c ...  linearily independant if the hypervolume a^b^c^... not = 0
F G linear functions
F(aa + bb) = aF(a) + bF(b)
F(a ^ b) = F(a) ^ F(b)  (outermorphism)
F(aA + bB) = aF(A) + bF(B)     (A B multivectors)
F(G(aa + bb))  = aF(G(a)) + bF(G(b))
F(G(aA + bB))  = aF(G(A)) + bF(G(B))
adjoint  :
definition :  a.adj(F(b)) = F(a).b
adj(F(a)) = ri a.F(fi)       ([r1,r2,r3] = reciprocal frame of [f1,f2,f3])
if orthonormal frame e1,e2,e3 (ri = ei) :
adj(F(a)) = e1 a.F(e1) + e2 a.F(e2) + e3 a.F(e3)
adj(adj(F(a)) = F(a)
adj(F(G(a)) = adj(G(adj(F(a)))        (adj FG --> adj G(adj F)       reverse the order
F symetrical function if adj(F(a)) = F(a)
F(adj(F(a)) and adj(F(F(a)) are symetrical functions
adj is a linear function and extend to arbitrary multivectors
determinant :
with I3  the unit pseudoscalar                         (e123 for   Cl3 orthonormal frame)
definition : F(I3) = det(F) I3
det( FG(I3)) = det(F) det(G) I3                      FG short script for F(G())
det(F) = det(adj(F))
inverse :
inv(F(A))         = I3 adj(F(inv(I3) A)) det(inv(F))
inv(adj(F(A)))  = I3      F(inv(I3) A)   det(inv(F))
eigenvectors and eigenblades  :
F has an eigen vector  e   if   F(e) = ae  with eigenvalue a (scalar)
det(F - aI3) = 0 wich define a polynomial equation for a
we extend the notion of eigenvector to that of an eigenblade :
F(Ak) = aAk      Ak is grade-k blade and a is real.
Each eigenblade determines an invariant subspace of the transformation.
    linear transformation

Lorentz transf. APS
Lorentz transf. STA
exterior algebra
linear transf.
conformal model
hogeneous model