Une application de l' orthogonalisation par Gram - Schmidt

P Reinhardt, LCT, UPMC

Les vecteurs donnés

a1={1,1,1}
a2={0,1,2}
a3={-1,1,-1}
a4={1,2,0}

L' orthogonalisation successive

a1pp=a1/Sqrt[3]

a2p=a2-a1pp.a2 a1pp//Simplify
a2pp=a2p/Norm[a2p]

a3p=a3-a1pp.a3 a1pp-a2pp.a3 a2pp//Simplify
a3pp=a3p/Norm[a3p]

a4p=a4-a1pp.a4 a1pp-a2pp.a4 a2pp-a3pp.a4 a3pp//Simplify