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]]

Call the eigvals() function:

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

The eigenvalues of the matrix are as follows:

Eigenvalues [ 2.  1.]

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]]

Check the result with the dot() function by calculating the right and left side of the eigenvalues equation...