How to formulate eigenvalues?

I'm using the following code to determine the eigenvalues for array A:

A = array([
    [1, 2],
    [4, 5]
])

eigenvals, eigenvecs = eig(A)

array([-0.46410162,  6.46410162])

When I do the calculation by hand, I have the following:

开发者_Python百科from matrix A, I have 1 - lambda, 2, and 4, 5 - lambda, which equals (1 - lambda)(4 - lambda) - 2*4 = 0, which results in x^2-3x-4=0

a = 1
b = -3
c = -4

-(-3) +- square root of -3^2 - 4(1)(-4) / 2 = 3 +- square root of 9 + 16 / 2 = 3 +- 5 / 2

equaling = 4 and -1

The python code gave me array([-0.46410162, 6.46410162]) for the eigenvalues, not 4, -1. What did I do wrong?

Your calculations are wrong.

from matrix A, I have 1 - lambda, 2, and 4, 5 - lambda, which equals (1 - lambda)(5 - lambda) - 2*4 = 0, which results in x^2-6x-3=0