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...