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x1=vector([2, 1]) x2=vector([1, -2]) 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([[7,2],[2,4]]) print C print print P.transpose()*C*P 

(2/5*sqrt(5), 1/5*sqrt(5))

(1/5*sqrt(5), -2/5*sqrt(5))

[ 2/5*sqrt(5)  1/5*sqrt(5)]
[ 1/5*sqrt(5) -2/5*sqrt(5)]

[7 2]
[2 4]

[8 0]
[0 3]

(2/5*sqrt(5), 1/5*sqrt(5))

(1/5*sqrt(5), -2/5*sqrt(5))

[ 2/5*sqrt(5)  1/5*sqrt(5)]
[ 1/5*sqrt(5) -2/5*sqrt(5)]

[7 2]
[2 4]

[8 0]
[0 3]