Gradient of Log-Determinant

Problem

Return the gradient of the log-determinant f(A) = log(det(A)) with respect to the 2x2 matrix A:

grad = inv(A)^T

Return None if det(A) == 0.

Hint

d/dA log det(A) = A^-T, the inverse transpose.

case 1

in: [[[1,2],[3,4]]]

expected: [[-2,1.5],[1,-0.5]]

case 2

in: [[[2,0],[0,3]]]

expected: [[0.5,0],[0,0.3333333333333333]]

case 3

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

expected: [[1,0],[0,1]]

case 4

in: [[[1,2],[2,4]]]

expected: null

Starter codePython

def grad_log_det_2x2(A):
    # Your code here
    pass

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