Time for action – determining eigenvalues and eigenvectors

Let's calculate the eigenvalues of a matrix:

1. Create a matrix as shown in the following:

   A = np.mat("3 -2;1 0")
   print("A\n", A)

   The matrix we created looks like the following:

   A
   [[ 3 -2]
    [ 1  0]]
   

2. Call the eigvals() function:

   print("Eigenvalues", np.linalg.eigvals(A))

   The eigenvalues of the matrix are as follows:

   Eigenvalues [ 2.  1.]
   

3. Determine eigenvalues and eigenvectors with the eig() function. This function returns a tuple, where the first element contains eigenvalues and the second element contains corresponding eigenvectors, arranged column-wise:

   eigenvalues, eigenvectors = np.linalg.eig(A)
   print("First tuple of eig", eigenvalues)
   print("Second tuple of eig\n", eigenvectors)

   The eigenvalues and eigenvectors appear as follows:

   First tuple of eig [ 2.  1.]
   Second tuple of eig
   [[ 0.89442719  0.70710678]
    [ 0.4472136   0.70710678]]
   

4. Check the result with the dot() function by calculating...