#
#
#  GramSchmidt - convert a set of linear vectors into an
#   orthonormal system
#
#					Gaston H. Gonnet (July 1998)
#
GramSchmidt := proc( A:matrix(numeric) )
r := [];
for z in A do
    for ri in r do z := z - (ri*z)*ri od;
    nz := z*z;
    if nz=0 then error('input vectors are linearly dependent') fi;
    r := append(r,z/sqrt(nz))
    od;
r
end: