{"cells":[{"metadata":{},"cell_type":"markdown","source":"# Chapitre 2, vecteurs propres et valeurs propres"},{"metadata":{},"cell_type":"markdown","source":"## Remarque.\n\nVoici le code pour calculer le spectre d'une matrice. N'hésitez pas à le tester pour vérifier vos calculs."},{"metadata":{"trusted":true},"cell_type":"code","source":"import numpy as np\nimport numpy.linalg as al \n # On importe la sous-bibliothèque linalg\n    \n    \nA=np.array([[1,3,0],[0,-2,0],[-1,-2,0]])\n # Entrez les coefficents de la matrice\n    \n    \nprint('Le spectre est :  ', al.eigvals(A))","execution_count":3,"outputs":[{"output_type":"stream","text":"Le spectre est :   [ 0.  1. -2.]\n","name":"stdout"}]},{"metadata":{},"cell_type":"markdown","source":"## Exercice \nExpliquez l'intérêt de la fonction Python suivante."},{"metadata":{"trusted":true},"cell_type":"code","source":"import numpy as np\nimport numpy.linalg as al \n\ndef bidule(A,x) : # A est une matrice carrée et x, un réel\n    [n,p]=np.shape(A)\n    if n!=p :\n        print('Non, la matrice n est pas carrée ...')\n    elif np.linalg.matrix_rank(A-x*np.eye(n))<n :\n        print('Oui !')\n    else :\n        print('Non !')","execution_count":6,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"# Un petit test\nJ2=np.ones([2,3])\nJ=np.ones([3,3])\nbidule(J2,1)\nbidule(J,-1)\nbidule(J,3)","execution_count":8,"outputs":[{"output_type":"stream","text":"Non, la matrice n est pas carrée ...\nNon !\noui !\n","name":"stdout"}]},{"metadata":{},"cell_type":"markdown","source":"## Exercice "},{"metadata":{"trusted":true},"cell_type":"code","source":"import numpy as np\nA = np.array([[1, 0, 0],[-2, 3, -2],[-1,1,0]])\nr1=np.linalg.matrix_rank(A-np.eye(3))\nr2=np.linalg.matrix_rank(A-2*np.eye(3))\nprint('r1=',r1,'r2=',r2)","execution_count":9,"outputs":[{"output_type":"stream","text":"r1= 1 r2= 2\n","name":"stdout"}]},{"metadata":{"trusted":true},"cell_type":"code","source":"","execution_count":null,"outputs":[]}],"metadata":{"kernelspec":{"name":"python3","display_name":"Python 3","language":"python"}},"nbformat":4,"nbformat_minor":2}