x1=vector([1,-1,2,0])
x2=vector([-2,1,0,1])
x3=vector([0,-1,4,1])
x4=vector([3,1,1,-1])
A=matrix([x1,x2,x3,x4])
[G,mu]=A.gram_schmidt()
B=matrix([G.row(i) / G.row(i).norm() for i in range(0, 3)]); B
print G
print
print B*B.transpose()
print
print B.transpose()*B
print
print B*B.transpose()==B.transpose()*B
|
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[ 1 -1 2 0]
[-3/2 1/2 1 1]
[ 1 19/9 5/9 -1/9]
[1 0 0]
[0 1 0]
[0 0 1]
[131/156 5/156 5/52 -55/156]
[ 5/156 155/156 -1/52 11/156]
[ 5/52 -1/52 49/52 11/52]
[-55/156 11/156 11/52 35/156]
False
[ 1 -1 2 0]
[-3/2 1/2 1 1]
[ 1 19/9 5/9 -1/9]
[1 0 0]
[0 1 0]
[0 0 1]
[131/156 5/156 5/52 -55/156]
[ 5/156 155/156 -1/52 11/156]
[ 5/52 -1/52 49/52 11/52]
[-55/156 11/156 11/52 35/156]
False
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