Factor Loadings from Correlation

Problem

Return the first principal component loadings of the 2-item correlation matrix [[1, r], [r, 1]]. For r >= 0 return [sqrt((1+r)/2), sqrt((1+r)/2)]; for r < 0 return [sqrt((1-r)/2), -sqrt((1-r)/2)].

Hint

Loadings equal the eigenvector scaled by the square root of its eigenvalue.

Test cases

case 1

in: [0.5]

expected: [0.8660254037844386,0.8660254037844386]

case 2

in: [0]

expected: [0.7071067811865476,0.7071067811865476]

case 3

in: [-0.5]

expected: [0.8660254037844386,-0.8660254037844386]

case 4

in: [1]

expected: [1,1]

case 5

in: [-1]

expected: [1,-1]

Starter codePython

def factor_loadings(r):
    # Your code here
    pass

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