Let's see how to compute the eigenvalues and eigenvectors for a 3x3 matrix. Evaluate the following code:
A = Matrix(QQ, [[2, -3, 1], [1, -2, 1], [1, -3, 2]])
print("Matrix A:")
show(A)
print("Eigenvalues:")
print(A.eigenvalues())
ev = A.eigenvectors_right()
for v in ev:
print("Eigenvalue: {0}".format(v[0]))
print(" Multiplicity: {0}".format(v[2]))
print(" Eigenvectors:")
for e in v[1]:
print(" " + str(e))
print("Eigenmatrices:")
D, P = A.eigenmatrix_right()
print("D:")
show(D)
print("P:")
show(P)
print(A*P == P*D)The output should look like this:
We defined a 3x3 matrix of rational numbers, and used the eigenvalues method to return a list of eigenvalues. We then used the eigenvectors_right method to return a list of tuples that contain data about the eigenvectors. We used a for loop to iterate through the list and print the information in a more readable format. Each element in...