Normalized Eigenvector 2x2

Problem

Return a unit eigenvector of the 2x2 matrix A for the given eigenvalue lam.

Form M = A - lam*I. Take the first row [a, b] of M with a nonzero entry, use [-b, a], and normalize it to unit L2 length. If M is the zero matrix, return [1.0, 0.0].

Hint

Any vector in the null space of A - lam*I is an eigenvector for lam.

Test cases

case 1

in: [[[2,0],[0,3]],2]

expected: [-1,0]

case 2

in: [[[4,1],[2,3]],5]

expected: [-0.7071067811865475,-0.7071067811865475]

case 3

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

expected: [-0.4472135954999579,0.8944271909999159]

case 4

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

expected: [1,0]

Starter codePython

def normalized_eigenvector(A, lam):
    # Your code here
    pass

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