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x1=vector([-2, 2]) x2=vector([5, 5]) a=x1.norm() b=x2.norm() z1=1/a*x1 z2=1/b*x2 print z1 print print z2 print P=column_matrix([z1, z2]) print P print C=matrix([[-3,6],[6,-3]]) print C print print P.transpose()*C*P 

(-1/2*sqrt(2), 1/2*sqrt(2))

(1/2*sqrt(2), 1/2*sqrt(2))

[-1/2*sqrt(2)  1/2*sqrt(2)]
[ 1/2*sqrt(2)  1/2*sqrt(2)]

[-3  6]
[ 6 -3]

[-9  0]
[ 0  3]

(-1/2*sqrt(2), 1/2*sqrt(2))

(1/2*sqrt(2), 1/2*sqrt(2))

[-1/2*sqrt(2)  1/2*sqrt(2)]
[ 1/2*sqrt(2)  1/2*sqrt(2)]

[-3  6]
[ 6 -3]

[-9  0]
[ 0  3]