MediumCalculusca-070

Eigenvalues of 2x2 Hessian

Problem

Compute the eigenvalues of the symmetric matrix H = [[p, q], [q, r]].

They are (p + r ± sqrt((p - r)^2 + 4*q^2)) / 2. Return them sorted in ascending order.

Hint

Symmetric matrices have real eigenvalues; use the discriminant formula and sort.

case 1

in: [2,0,2]

expected: [2,2]

case 2

in: [4,1,4]

expected: [3,5]

case 3

in: [1,2,1]

expected: [-1,3]

case 4

in: [-2,0,-8]

expected: [-8,-2]

case 5

in: [3,4,3]

expected: [-1,7]

Starter codePython

def hessian_eigenvalues(p, q, r):
    # Return [smaller, larger]
    # Your code here
    pass

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