MediumCalculusca-031

Hessian of a Quadratic Form

Problem

Return the constant Hessian matrix of f(x, y) = a * x^2 + b * x * y + c * y^2 as a 2x2 nested list.

The matrix is [[2a, b], [b, 2c]] since all second partials are constants.

Hint

Mixed partials are equal for this smooth function, so the Hessian is symmetric.

case 1

in: [1,2,3]

expected: [[2,2],[2,6]]

case 2

in: [-1,0,2]

expected: [[-2,0],[0,4]]

case 3

in: [0,5,0]

expected: [[0,5],[5,0]]

case 4

in: [2,-3,2]

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

Starter codePython

def quadratic_hessian(a, b, c):
    # Return [[H_xx, H_xy], [H_yx, H_yy]]
    # Your code here
    pass

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