# Mathematics > Linear Algebra Foundations > Linear Algebra Foundations #9 - Eigenvalues
# Compute the Eigenvalues of the following 2x2 matrix.
#
# https://www.hackerrank.com/challenges/linear-algebra-fundamentals-9-eigenvalues/problem
#

# http://mathworld.wolfram.com/Eigenvalue.html

Définition générale
  det(A-λI) = 0

Solution générale pour dim=2
  λ = 1/2 [ (a11 + a22] ± sqrt(4 * a12 * a21 + (a11 - a22)^2) ]

Solution avec numpy
  print(np.linalg.eigvals(np.matrix([[0, 1],[ -2, -3]])))

Solution calulée:
  A = [0   1]
      [-2 -3]
  λ = 1/2 * (-3 ± sqrt(-8+3^2))
  ⟹ λ₁ = -4/2 = -2
  ⟹ λ₂ = -2/2 = -1

Réponse:

-2
-1