x1=vector([1,1,0])
x2=vector([0,1,2])
x3=vector([1,2,2])
A=matrix([x1,x2,x3])
[G,mu]=A.gram_schmidt()
B=matrix([G.row(i) / G.row(i).norm() for i in range(0, 2)]); B
P1= B*B.transpose()
P2= B.transpose()*B
print G
print
print
print P1
print
print P2
print
print P1==P2
|
|
[ 1 1 0]
[-1/2 1/2 2]
[1 0]
[0 1]
[ 5/9 4/9 -2/9]
[ 4/9 5/9 2/9]
[-2/9 2/9 8/9]
False
[ 1 1 0]
[-1/2 1/2 2]
[1 0]
[0 1]
[ 5/9 4/9 -2/9]
[ 4/9 5/9 2/9]
[-2/9 2/9 8/9]
False
|