diff --git a/math_linear_algebra.ipynb b/math_linear_algebra.ipynb
index 0d937e0..629b175 100644
--- a/math_linear_algebra.ipynb
+++ b/math_linear_algebra.ipynb
@@ -230,6 +230,7 @@
    "outputs": [
     {
      "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW0AAAD8CAYAAAC8TPVwAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAAPDUlEQVR4nO3db2xd9X3H8fc3/whwQUFgCsVAilpHQ0gFEmgLKqqhq2iLqIZWCaRWWrXJe9AhGKvGuiej2oNpFarGgw4JAR1qgcoLoK7pxmDKZagI6OKEPwEz1qQZePxXx58LTZos3z24NyKxHd+T2Nfn/OD9kq64NifoI8t5+/r4HBOZiSSpDEvqHiBJqs5oS1JBjLYkFcRoS1JBjLYkFcRoS1JBKkU7IlZFxPqIeC4iJiPiM4MeJkmaaVnF424C7s/M34+IFcBRA9wkSTqI6HdzTUQcCzwJnJHeiSNJtarySvsM4HXgBxHxSWACuCYz393/oIgYA8YAVq5cufa0005b6K3zsnfvXpYsadYpfDdV08RN0MxdbqqmiZuef/75NzJzqO+BmTnnA1gH7AE+1Xv7JuCv5/ozIyMj2TTtdrvuCTO4qZombsps5i43VdPETcCm7NPjzKz0g8gpYCozH++9vR449zC+kEiS5qlvtDPzFeDFiFjTe9clwLMDXSVJmlXVq0euBu7sXTmyHfjG4CZJkg6mUrQz8wm657YlSTVq1o9PJUlzMtqSVBCjLUkFMdqSVBCjLUkFMdqSVBCjLUkFMdqSVBCjLUkFMdqSVBCjLUkFMdqSVBCjLUkFMdqSVBCjLUkFMdqSVBCjLUkFMdqSVBCjLUkFMdqSVBCjLUkFMdqSVBCjLUkFMdqSVBCjLUkFMdqSVBCjLUkFqRTtiNgREU9HxBMRsWnQoz7Q3noLrr0WTjoJnnoKrr8e3n237lWSCrHsEI4dzcw3Brbkw2DPHrjgAti2DXbtgt274aaboN2Gxx6DJX7jI2luVmIx/fSn8MIL3WDvs2sXTE7Cxo317ZJUjKrRTuCBiJiIiLFBDvpAm5iATmfm+3fuhC1bFn+PpOJEZvY/KOKjmflSRJwIPAhcnZkPTztmDBgDGBoaWjs+Pj6IvYet0+nQarXqHfHGG/Dii7B3b3fT8DCtqanuaZHVq+G44+rdR0M+TtM0cRM0c5ebqmniptHR0YnMXNf3wMw8pAdwA/CtuY4ZGRnJpmm323VPyHznnczjj8+MyIRs33hj5pIlmSefnLlzZ93rMrMhH6dpmrgps5m73FRNEzcBm7JCg/ueHomIoyPimH3PgS8AW+fzFeVDq9WCRx6B88+H5cshovuDyUcegSOOqHudpAJUuXrkI8B9EbHv+Lsy8/6BrvogW7Ome6XIm2/C5s1w3XV1L5JUkL7RzsztwCcXYcuHy6pVXuIn6ZBZDUkqiNGWpIIYbUkqiNGWpIIYbUkqiNGWpIIYbUkqiNGWpIIYbUkqiNGWpIIYbUkqiNGWpIIYbUkqiNGWpIIYbUkqiNGWpIIYbUkqiNGWpIIYbUkqiNGWpIIYbUkqiNGWpIIYbUkqiNGWpIIYbUkqiNGWpIIYbUkqiNGWpIJUjnZELI2ILRGxYZCDJEkHdyivtK8BJgc1RJLUX6VoR8Qw8GXg1sHOkSTNJTKz/0ER64G/AY4BvpWZl81yzBgwBjA0NLR2fHx8gafOT6fTodVq1T3jAG6qpomboJm73FRNEzeNjo5OZOa6vgdm5pwP4DLg73vPPwds6PdnRkZGsmna7XbdE2ZwUzVN3JTZzF1uqqaJm4BN2aetmVnp9MiFwOURsQP4MXBxRPzo8L6WSJLmo2+0M/PbmTmcmauBK4GNmfm1gS+TJM3gddqSVJBlh3JwZj4EPDSQJZKkvnylLUkFMdqSVBCjLUkFMdqSVBCjLUkFMdqSVBCjLUkFMdqSVBCjLUkFMdqSVBCjLUkFMdqSVBCjLUkFMdqSVBCjLUkFMdqSVBCjLUkFMdqSVBCjLUkFMdqSVBCjLUkFMdqSVBCjLUkFMdqSVBCjLUkFMdqSVBCjLUkF6RvtiFgZEb+IiCcj4pmI+M5iDJMkzbSswjG7gIszsxMRy4GfR8S/ZOZjA94mSZqmb7QzM4FO783lvUcOcpQkaXbRbXKfgyKWAhPAx4HvZ+b1sxwzBowBDA0NrR0fH1/gqfPT6XRotVp1zziAm6pp4iZo5i43VdPETaOjoxOZua7vgZlZ+QGsAtrAWXMdNzIykk3TbrfrnjCDm6pp4qbMZu5yUzVN3ARsygodPqSrRzLzTeAh4NJD/CIiSVoAVa4eGYqIVb3nRwKfB54b8C5J0iyqXD1yMnBH77z2EmA8MzcMdpYkaTZVrh55CjhnEbZIkvrwjkhJKojRlqSCGG1JKojRlqSCGG1JKojRlqSCGG1JKojRlqSCGG1JKojRlqSCGG1JKojRlqSCGG1JKojRlqSCGG1JKojRlqSCGG1JKojRlqSCGG1JKojRlqSCGG1JKojRlqSCGG1JKojRlqSCGG1JKojRlqSCGG1JKkjfaEfEqRHRjojJiHgmIq5ZjGGSpJmWVThmD/Bnmbk5Io4BJiLiwcx8dsDbJEnT9H2lnZkvZ+bm3vN3gEnglEEPkyTNFJlZ/eCI1cDDwFmZ+fa0fzcGjAEMDQ2tHR8fX8CZ89fpdGi1WnXPOICbqmniJmjmLjdV08RNo6OjE5m5ru+BmVnpAbSACeCKfseOjIxk07Tb7bonzOCmapq4KbOZu9xUTRM3AZuyQosrXT0SEcuBe4A7M/Pew/9aIkmajypXjwRwGzCZmd8b/CRJ0sFUeaV9IfB14OKIeKL3+NKAd0mSZtH3kr/M/DkQi7BFktSHd0RKUkGMtiQVxGhLUkGMtiQVxGhLUkGMtiQVxGhLUkGMtiQVxGhLUkGMtiQVxGhLUkGMtiQVxGhLUkGMtiQVxGhLUkGMtiQVxGhLUkGMtiQVxGhLUkGMtiQVxGhLUkGMtiQVxGhLUkGMtiQVxGhLUkGMtiQVxGhLUkH6Rjsibo+I1yJi62IM0uLbvRtuuAFOOgm2bIErroDt2+teJWk2VV5p/wNw6YB3qEZXXQXf/S68+irs3Qs/+Qmcdx68/nrdyyRN1zfamfkw8OtF2KIabNsGP/sZ/OY3779v71547z24+eb6dkmanee0P+SefhpWrJj5/p074dFHF3+PpLlFZvY/KGI1sCEzz5rjmDFgDGBoaGjt+Pj4Qm1cEJ1Oh1arVfeMAzRh086dMDnZfXUNMDzcYWqqRQSceCIMD9c6D2jGx2k2TdzlpmqauGl0dHQiM9f1PTAz+z6A1cDWKsdmJiMjI9k07Xa77gkzNGXTZz+becQRmZB5443thMxWK3PHjrqXdTXl4zRdE3e5qZombgI2ZYW+enpEbNgAX/3q+6dJzj4bNm6E00+vdZakWVS55O9u4FFgTURMRcQfDn6WFtOxx8IPfwidDpxzTveyv/POq3uVpNks63dAZl61GENUv+XLYYnfe0mN5l9RSSqI0ZakghhtSSqI0ZakghhtSSqI0ZakghhtSSqI0ZakghhtSSqI0ZakghhtSSqI0ZakghhtSSqI0ZakghhtSSqI0ZakghhtSSqI0ZakghhtSSqI0ZakghhtSSqI0ZakghhtSSqI0ZakghhtSSqI0ZakghhtSSqI0ZakglSKdkRcGhH/GRG/jIi/GPQoSdLs+kY7IpYC3we+CJwJXBURZw56mCRppiqvtM8HfpmZ2zPzt8CPga8MdpYkaTbLKhxzCvDifm9PAZ+aflBEjAFjvTd3RcTW+c9bUCcAb9Q9Yho3VdPETdDMXW6qpomb1lQ5qEq0Y5b35Yx3ZN4C3AIQEZsyc12VAYvFTdW4qbom7nJTNU3dVOW4KqdHpoBT93t7GHjpcEZJkuanSrT/A/hERHwsIlYAVwL/NNhZkqTZ9D09kpl7IuJPgH8FlgK3Z+Yzff7YLQsxboG5qRo3VdfEXW6qpthNkTnj9LQkqaG8I1KSCmK0JakgCxrtJt7uHhG3R8RrTbpuPCJOjYh2RExGxDMRcU0DNq2MiF9ExJO9Td+pe9M+EbE0IrZExIa6twBExI6IeDoinqh6mdagRcSqiFgfEc/1Pq8+04BNa3ofo32PtyPi2gbs+tPe5/jWiLg7IlY2YNM1vT3P9P0YZeaCPOj+kHIbcAawAngSOHOh/vvz2HURcC6wte4t+206GTi39/wY4Pm6P1Z0r8dv9Z4vBx4HPl33x6q35zrgLmBD3Vt6e3YAJ9S9Y9qmO4A/6j1fAayqe9O0fUuBV4DTa95xCvAr4Mje2+PAH9S86SxgK3AU3YtD/g34xMGOX8hX2o283T0zHwZ+XfeO/WXmy5m5uff8HWCS7idTnZsyMzu9N5f3HrX/lDoihoEvA7fWvaWpIuJYui9ObgPIzN9m5pu1jprpEmBbZv533UPohvHIiFhGN5R133fyO8BjmfleZu4B/h34vYMdvJDRnu1291pDVIKIWA2cQ/eVba16pyGeAF4DHszM2jcBfwf8ObC35h37S+CBiJjo/fqGup0BvA78oHca6daIOLruUdNcCdxd94jM/B/gRuAF4GXgrcx8oN5VbAUuiojjI+Io4EsceEPjARYy2pVud9f7IqIF3ANcm5lv170nM/8vM8+me9fr+RFxVp17IuIy4LXMnKhzxywuzMxz6f7my29GxEU171lG9xTgzZl5DvAu0IifKQH0bsq7HPjHBmw5ju4ZgI8BHwWOjoiv1bkpMyeBvwUeBO6ne2p5z8GOX8hoe7v7IYiI5XSDfWdm3lv3nv31vrV+CLi03iVcCFweETvonm67OCJ+VO8kyMyXev98DbiP7qnBOk0BU/t9Z7SebsSb4ovA5sx8te4hwOeBX2Xm65m5G7gXuKDmTWTmbZl5bmZeRPd07n8d7NiFjLa3u1cUEUH3/ONkZn6v7j0AETEUEat6z4+k+8n9XJ2bMvPbmTmcmavpfj5tzMxaXxVFxNERccy+58AX6H57W5vMfAV4MSL2/Za4S4Bna5w03VU04NRIzwvApyPiqN7fw0vo/kypVhFxYu+fpwFXMMfHq8pv+askD+9294GLiLuBzwEnRMQU8FeZeVu9q7gQ+DrwdO8cMsBfZuY/1zeJk4E7ev/TiyXAeGY24hK7hvkIcF/37zvLgLsy8/56JwFwNXBn7wXTduAbNe8BoHeO9neBP657C0BmPh4R64HNdE9BbKEZt7TfExHHA7uBb2bm/x7sQG9jl6SCeEekJBXEaEtSQYy2JBXEaEtSQYy2JBXEaEtSQYy2JBXk/wEjMkAxy5qSRgAAAABJRU5ErkJggg==\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -773,8 +774,8 @@
     "## Zero, unit and normalized vectors\n",
     "* A **zero-vector** is a vector full of 0s.\n",
     "* A **unit vector** is a vector with a norm equal to 1.\n",
+    "* The **normalized vector** of a non-null vector $\\textbf{v}$, noted $\\hat{\\textbf{v}}$, is the unit vector that points in the same direction as $\\textbf{v}$. It is equal to: $\\hat{\\textbf{v}} = \\dfrac{\\textbf{v}}{\\left \\Vert \\textbf{v} \\right \\|}$\n",
     "\n"
-    "* The **normalized vector** of a non-null vector $\\textbf{v}$, noted $\\hat{\\textbf{v}}$, is the unit vector that points in the same direction as $\\textbf{v}$. It is equal to: $\\hat{\\textbf{v}} = \\dfrac{\\textbf{v}}{\\left \\Vert \\textbf{v} \\right \\|}$\n"
    ]
   },
   {