Diagonalizability via Distinct Eigenvalues

Problem

Decide whether a 2x2 matrix A is diagonalizable over the reals.

If the eigenvalues are real and distinct (discriminant > 1e-9), return True. If the eigenvalue is repeated, A is diagonalizable only when A is that scalar multiple of the identity. Otherwise return False.

Hint

A repeated eigenvalue needs a full set of two independent eigenvectors.

Test cases

case 1

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

expected: true

case 2

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

expected: false

case 3

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

expected: true

case 4

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

expected: false

Starter codePython

def is_diagonalizable_2x2(A):
    # Your code here
    pass

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