A=matrix([[1,-1],[-1,1]])
print A.eigenvectors_right()
print
x1=vector([1,-1])
x2=vector([1,1])
a=x1.norm()
b=x2.norm()
z1=1/a*x1
z2=1/b*x2
P=column_matrix([z1, z2])
print P
print
C=matrix([[1,-1],[-1,1]])
print P.transpose()*C*P
print
|
|
[(2, [
(1, -1)
], 1), (0, [
(1, 1)
], 1)]
[ 1/2*sqrt(2) 1/2*sqrt(2)]
[-1/2*sqrt(2) 1/2*sqrt(2)]
[2 0]
[0 0]
[(2, [
(1, -1)
], 1), (0, [
(1, 1)
], 1)]
[ 1/2*sqrt(2) 1/2*sqrt(2)]
[-1/2*sqrt(2) 1/2*sqrt(2)]
[2 0]
[0 0]
|