Gradient of the Determinant (Matrix Calculus)

Problem

For the 2x2 matrix A = [[a, b], [c, d]], the gradient of the determinant with respect to the entries is the cofactor matrix.

Since det(A) = a*d - b*c, return [[d, -c], [-b, a]] as a nested list of floats.

Hint

Each partial derivative is the cofactor of the corresponding entry.

case 1

in: [1,2,3,4]

expected: [[4,-3],[-2,1]]

case 2

in: [2,0,0,3]

expected: [[3,0],[0,2]]

case 3

in: [1,1,1,1]

expected: [[1,-1],[-1,1]]

case 4

in: [0,0,0,0]

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

Starter codePython

def gradient_det(a, b, c, d):
    # Return the 2x2 gradient of det(A)
    # Your code here
    pass

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