Hilbert 2x2 Condition Number

Problem

Return the 2-norm condition number of the n x n Hilbert matrix, for n = 1 or 2.

For n = 2, the matrix [[1, 1/2], [1/2, 1/3]] is symmetric positive definite with eigenvalues (4 +/- sqrt(13)) / 6, so the condition number is their ratio. Return None for any other n.

Hint

For a symmetric positive definite matrix, the 2-norm condition number is the ratio of extreme eigenvalues.

Test cases

case 1

in: [1]

expected: 1

case 2

in: [2]

expected: 19.281470067903985

case 3

in: [0]

expected: null

case 4

in: [3]

expected: null

Starter codePython

def hilbert_condition(n):
    # Your code here
    pass

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