MediumCalculusca-237

Trace AXB Gradient

Problem

For the scalar function f(X) = trace(A X B) with constant 2x2 matrices A and B, the gradient with respect to X is A^T B^T.

Given the entries of A (a, b, c, d) and B (e, f, g, h), return the 2x2 gradient as a nested list.

Hint

Write the trace as a sum over indices and differentiate entry by entry.

case 1

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

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

case 2

in: [1,2,3,4,5,6,7,8]

expected: [[23,31],[34,46]]

case 3

in: [0,0,0,0,1,2,3,4]

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

case 4

in: [1,0,0,2,0,1,1,0]

expected: [[0,1],[2,0]]

Starter codePython

def trace_axb_gradient(a, b, c, d, e, f, g, h):
    # Return the 2x2 gradient
    # Your code here
    pass

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