Linear Algebra and the C Language/a0pj

__NOTOC__ Linear discrete dynamical system (eigen) Let : u_n+1 = a11 u_n + a12 v_n v_n+1 = a21 u_n + a22 v_n If you write : (t : transpose) X_n = [u_n, v_n]t and then X_n+1 = A X_n X_n+1 = [u_n+1,v_n+1]t Let's put X_0 = [u_0,v_0]t then X_1 = A X_0 X_2 = A X_1 = A^2 X_0 X_3 = A X_2 = A^3 X_0 ... X_n = A^n X_0 Calculate : lim X_n = n-> oo For this, we will use eigenvalues ​​and eigenvectors for the first method, and for the second method we will directly calculate the power of A. Exemple 1 : c00a.c : Let's calculate the eigenvectors and eigenvalues c00b.c : Calculate A^P We will be able to observe that from P = 19, the value of A^P no longer changes. Exemple 2 : c00c.c : Let's calculate the eigenvectors and eigenvalues c00d.c Calculate A^P We will be able to observe that from P = 17, the value of A^P no longer changes.