for a, b, c, ia, ib, ic being non zero Element of F_Real
for P being Point of (ProjectiveSpace (TOP-REAL 3))
for N being invertible Matrix of 3,F_Real st P = Dir |[a,b,c]| & ia = 1 / a & ib = 1 / b & ic = 1 / c & N = <*<*ia,0,0*>,<*0,ib,0*>,<*0,0,ic*>*> holds
(homography N) . P = Dir |[1,1,1]|