Singular Values 2x2

Problem

Compute the singular values of a 2x2 matrix A as the square roots of the eigenvalues of A^T A.

Return [larger, smaller] as floats. Singular values are non-negative even when a numerical eigenvalue is slightly negative.

Hint

A^T A is symmetric positive semidefinite, so its eigenvalues are non-negative.

case 1

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

expected: [2,1]

case 2

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

expected: [4,3]

case 3

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

expected: [1.4142135623730951,0]

case 4

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

expected: [5.464985704219043,0.3659661906262571]

Starter codePython

def singular_values_2x2(A):
    # Your code here
    pass

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