What are the advantages of using numpy.identity over numpy.eye?

identity just calls eye so there is no difference in how the arrays are constructed. Here's the code for identity:

def identity(n, dtype=None):
    from numpy import eye
    return eye(n, dtype=dtype)

As you say, the main difference is that with eye the diagonal can may be offset, whereas identity only fills the main diagonal.

Since the identity matrix is such a common construct in mathematics, it seems the main advantage of using identity is for its name alone.

To see the difference in an example, run the below codes:

import numpy as np

#Creates an array of 4 x 4 with the main diagonal of 1

arr1 = np.eye(4)
print(arr1)

print("\n")

#or you can change the diagonal position

arr2 = np.eye(4, k=1)  # or try with another number like k= -2
print(arr2)

print("\n")

#but you can't change the diagonal in identity

arr3 = np.identity(4)
print(arr3)