Matrix Square Root 2x2

Problem

Compute the unique symmetric positive definite square root S of a symmetric positive definite 2x2 matrix A, so that S*S = A.

Use the eigendecomposition A = Q*Lambda*Q^T with orthonormal Q and return S = Q*sqrt(Lambda)*Q^T.

Hint

Take square roots of the eigenvalues while keeping the eigenvectors unchanged.

case 1

in: [[[4,0],[0,9]]]

expected: [[2,0],[0,3]]

case 2

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

expected: [[1,0],[0,1]]

case 3

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

expected: [[1.3660254037844384,0.3660254037844386],[0.3660254037844386,1.3660254037844384]]

case 4

in: [[[5,4],[4,5]]]

expected: [[2,1],[1,2]]

Starter codePython

def matrix_sqrt_2x2(A):
    # Your code here
    pass

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