Eigenvector via Row Cross Product

Problem

Find an eigenvector of an integer 3x3 matrix A for the given eigenvalue lam.

Form M = A - lam*I and take the cross product of two rows of M, which lies in the null space when those rows span the row space. Try row pairs (0,1), (0,2), (1,2) in order, returning the first nonzero cross product w with M*w exactly zero, or None if no pair works.

Hint

The cross product of two rows of M = A - lam*I is orthogonal to the row space, hence in the null space.

Test cases

case 1

in: [[[2,1,0],[0,3,0],[0,0,4]],2]

expected: [2,0,0]

case 2

in: [[[2,1,0],[0,3,0],[0,0,4]],3]

expected: [1,1,0]

case 3

in: [[[2,1,0],[0,3,0],[0,0,4]],4]

expected: [0,0,2]

case 4

in: [[[2,1,0],[0,3,0],[0,0,4]],1]

expected: null

case 5

in: [[[3,1,0],[0,3,0],[0,0,1]],1]

expected: [0,0,4]

Starter codePython

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

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