Gradient of the Frobenius Norm

Problem

For a nonzero matrix X, the gradient of the Frobenius norm ||X||_F = sqrt(sum of squared entries) is X / ||X||_F.

Given a matrix as a nested list, return the gradient with the same shape. Return the zero matrix when all entries are zero.

Hint

The gradient points along the matrix itself with length one.

case 1

in: [[[3,4],[0,0]]]

expected: [[0.6,0.8],[0,0]]

case 2

in: [[[1,0],[0,1]]]

expected: [[0.7071067811865475,0],[0,0.7071067811865475]]

case 3

in: [[[0,0],[0,0]]]

expected: [[0,0],[0,0]]

case 4

in: [[[2]]]

expected: [[1]]

Starter codePython

def frobenius_norm_gradient(matrix):
    # Your code here
    pass

4 test cases · run your code against them in the editor