Eigenvalue Certificate Check

Problem

Check whether lam is an eigenvalue of A by testing whether det(A - lam*I) is zero.

Subtract lam along the diagonal, compute the determinant for matrices of size 1, 2, or 3 by cofactor expansion, and return True if the absolute determinant is below 1e-9.

Hint

lam is an eigenvalue exactly when A - lam*I is singular.

Test cases

case 1

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

expected: true

case 2

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

expected: false

case 3

in: [[[1,2,3],[0,4,5],[0,0,6]],4]

expected: true

case 4

in: [[[1,2,3],[0,4,5],[0,0,6]],2]

expected: false

case 5

in: [[[7]],7]

expected: true

Starter codePython

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

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