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   "source": [
   "import numpy as np\n",
   "import matplotlib.pyplot as plt\n",
   "import scipy.linalg as la\n",
   "\n",
   "#a function that takes a matrix, calculates the eigenvalues, the eigenvectors, and for each of the pairs of eigenvalue and eigenvector\n",
   "# validates if A*v==lambda*v\n",
   "\n",
   "def check_validity(A):\n",
   " eigvals, eigvecs = la.eig(A) #calculatues eigenvalues & eigenvectors of A\n",
   " dim1=A.shape[0] #used later for the first dimension when reshaping the eigenvector: 2 for 2x2 matrces and 3 for 3x3\n",
   " j=0 #iterator\n",
   " while(j<len(eigvals)):\n",
   " lambda_j=eigvals[j] #jth eigenvalue\n",
   " v_j=eigvecs[:,j].reshape(dim1,1) #jth eigenvector\n",
   "\n",
   " product_1=lambda_j * v_j #first of the two products to be validated: eigenvalue times the eigenvector\n",
   " product_2=(A@ v_j) #second product: the matrix times the eigenvector\n",
   " print(\"Eigenvalue \"+str(j+1)+\" is \"+str(lambda_j)+\". Eigenvector\"+str(j+1)+\" is\"+str(eigvecs[:,j])+\"\\n\")\n",
   " print(\"The left product is:\\n \"+ str(product_2))\n",
   " print(\"The right product is:\\n\"+str(product_1))\n",
   " print(\"We can see they are equal!\\n\\n\")\n",
   "\n",
   " j=j+1 \n"
   ],

Introduction - Main Function Go is a fairly old Chinese board game...