Spectral Gap 2x2

Problem

Compute the spectral gap of a 2x2 matrix with real eigenvalues:

gap = |lambda1| - |lambda2|, where lambda1 and lambda2 are the eigenvalues from the characteristic polynomial.

Return None if the discriminant is negative (complex eigenvalues).

Hint

The gap determines how fast power iteration converges.

case 1

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

expected: 2

case 2

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

expected: 2

case 3

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

expected: 3

case 4

in: [[[1,1],[-1,1]]]

expected: null

Starter codePython

def spectral_gap_2x2(A):
    # Your code here
    pass

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