:: deftheorem Def02 defines line_homography BKMODEL3:def 2 :
for N being invertible Matrix of 3,F_Real
for b₂ being Function of the Lines of (IncProjSp_of real_projective_plane), the Lines of (IncProjSp_of real_projective_plane) holds
( b₂ = line_homography N iff for x being LINE of (IncProjSp_of real_projective_plane) holds b₂ . x = { ((homography N) . P) where P is POINT of (IncProjSp_of real_projective_plane) : P on x } );