def find_eigenvalues_by_scanning(A, low=-10, high=10, step=0.001):
    n = len(A)
    identity = np.eye(n)
    found = []
    prev_sign = None
    lam = low

    while lam <= high:
        test_matrix = A - lam * identity
        value = det(test_matrix)
        current_sign = value > 0

        if prev_sign is not None and current_sign != prev_sign:
            found.append(round(lam, 2))

        prev_sign = current_sign
        lam += step

    return found


A = np.array([[2, 1],
              [1, 2]])

print(find_eigenvalues_by_scanning(A))

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