A = matrix([[3,-4],[-4,3]])
print A
print
print A.eigenvalues()
E = identity_matrix(2)
print
print (A-7*E).echelon_form()
print
print (A+E).echelon_form()
point
x1 = vector([1,-1])
x2 = vector([1,1])
P = column_matrix([x1, x2])
print
print P
print
print P^-1*A*P
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[ 3 -4]
[-4 3]
[7, -1]
[4 4]
[0 0]
[ 4 -4]
[ 0 0]
[ 1 1]
[-1 1]
[ 7 0]
[ 0 -1]
[ 3 -4]
[-4 3]
[7, -1]
[4 4]
[0 0]
[ 4 -4]
[ 0 0]
[ 1 1]
[-1 1]
[ 7 0]
[ 0 -1]
|