How to calculate the Frobenius inner product of two matrices using Python NumPy?

We can use the following Python code to calculate the Frobenius inner product of two matrices.

import numpy

m = 2
n = 3

A = numpy.random.randint(low=1, high=10, size=(m, n))
B = numpy.random.randint(low=1, high=10, size=(m, n))

f = numpy.trace(numpy.matmul(A.transpose(), B))

print("A: \n", A)
print("B: \n", B)
print("The Frobenius inner product of A and B: ", f)

Here, we are first creating two matrices A and B that contain random integers. We are using the numpy.random.randint() function for that purpose. The generated random integers will be within the range [low, high). And the size of the matrix is given by the size argument. For example, size=(m, n) specifies that the created matrix will have m rows and n columns.

A = numpy.random.randint(low=1, high=10, size=(m, n))
B = numpy.random.randint(low=1, high=10, size=(m, n))

Now, we are calculating the matrix ATB. Then, we are finding out the value of the trace of the matrix ATB.

f = numpy.trace(numpy.matmul(A.transpose(), B))

The result f is the Frobenius inner product of the two matrices A and B. The output of the mentioned program will be:

A: 
 [[2 9 7]
 [2 3 8]]
B: 
 [[1 8 8]
 [2 5 3]]
The Frobenius inner product of A and B:  173