B = matrix([[2,1,1],[1,2,1], [1,1,2]])
print B
print
print B.eigenvalues()
E = identity_matrix(3)
print
print (B-4*E).echelon_form()
print
print (B-E).echelon_form()
print
print (B-E).echelon_form()
x1 = vector([1,1,1])
x2 = vector([-1,1,0])
x3 = vector([-1,0,1])
P = column_matrix([x1, x2, x3])
print
print P
print
print P^-1*B*P
|
[2 1 1]
[1 2 1]
[1 1 2]
[4, 1, 1]
[ 1 1 -2]
[ 0 3 -3]
[ 0 0 0]
[1 1 1]
[0 0 0]
[0 0 0]
[1 1 1]
[0 0 0]
[0 0 0]
[ 1 -1 -1]
[ 1 1 0]
[ 1 0 1]
[4 0 0]
[0 1 0]
[0 0 1]
[2 1 1]
[1 2 1]
[1 1 2]
[4, 1, 1]
[ 1 1 -2]
[ 0 3 -3]
[ 0 0 0]
[1 1 1]
[0 0 0]
[0 0 0]
[1 1 1]
[0 0 0]
[0 0 0]
[ 1 -1 -1]
[ 1 1 0]
[ 1 0 1]
[4 0 0]
[0 1 0]
[0 0 1]
|