In SciPy, we calculate the eigenvector and eigenvalue of a given matrix by using the eig function in scipy.linalg.

Using the following code, let us look at calculating the eigenvector and the corresponding eigenvalue of a given matrix:

1. Initialize a matrix:

a = np.array([[1, 2], [3, 4]])

2. Calculate the eigenvalue and eigenvector of the matrix:

la, v = linalg.eig(a)

3. The output of the preceding code is:

print(la)
[-0.37228132+0.j  5.37228132+0.j]
print(v)
[[-0.82456484 -0.41597356] [ 0.56576746 -0.90937671]]

Note that la is the eigenvalue and the  v matrix is the eigenvector.

Let us cross-check the preceding output based on the intuition we laid out at the start of this section.

The eigenvector for a given matrix A satisfies the following criterion:

The following applies:

• A is the matrix
• v is the eigenvector
• λ is the eigenvalue

Let us cross-check the output based on the intuition we laid out earlier.

1. Calculate the value of the matrix multiplication of A•v:

np.dot(a,v)
array([[ 0.30697009, -2.23472698],       [-0.21062466, -4.88542751]])

2. Calculate the value of the matrix multiplication of λ v:

la*v
array([[ 0.30697009-0.j, -2.23472698+0.j],
       [-0.21062466+0.j, -4.88542751+0.j]])

Note that the output satisfies the initially laid out equation: A•v = λ v.