cosmetic

diagonalized lambdas and factorisation.py

A = np.array([[1, 4], [2, 3]])
lambdas, eigenVectors = np.linalg.eig(A)
eigenVectors = Scaling_Eigen_Vectors(eigenVectors= eigenVectors)
print('lambdas: \n', lambdas)
Λ = np.around(np.linalg.inv(eigenVectors).dot(A).dot(eigenVectors),
              decimals= 8)
print('diagonalized lambdas (Λ): \n', Λ)
# power of matrix = 20
print('With factorization: \n', eigenVectors.dot(Λ**20).dot(np.linalg.inv(eigenVectors)))
print('Without factorization: \n', M .dot(M).dot(M).dot(M).dot(M).dot(M).
                               dot(M).dot(M).dot(M).dot(M).dot(M).dot(M)
                              .dot(M).dot(M).dot(M).dot(M).dot(M).dot(M)
                              .dot(M).dot(M))


Output:
lambdas: 
 [-1.  5.]
 
diagonalized lambdas (Λ): 
 [[-1.  0.]
 [ 0.  5.]]

With factorization: 
 [[3.69159090e+16  5.44817274e+16  9.34547768e+16]
 [4.41426087e+16  6.51471315e+16  1.11749589e+17]
 [9.86243361e+16  1.45553079e+17  2.49673259e+17]]

Without factorization: 
 [[ 36915909407920134  54481728070503621  93454777850116815]
 [ 44142609209910003  65147132222165457 111749589908542773]
 [ 98624337280413624 145553080257859158 249673262259637809]]