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     "name": "stdout",
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     "text": [
      "Matrix A:\n",
      " [[ 8  8 10  0 -1 11 -2  2  7]\n",
      " [ 1 11  4  2  7  4 12 11  9]\n",
      " [-2 -3  5  9  8  6  9 -1  5]\n",
      " [10  2  8  6  8  7  3  3 -2]\n",
      " [12  5  8 -3 -1 12  7 -4  1]] \n",
      "\n",
      "Vector v:\n",
      " [[8 6 7 8 5]] \n",
      "\n",
      "v@A:\n",
      " [[196 150 243 108 149 270 178  79 134]] \n",
      "\n",
      "||v@A||\n",
      " 531.6117003979502\n",
      "Frobenius norm of A (tr(A@A.T)): \n",
      " 2078\n",
      "||v||*||A_f||:  32057.822633485262 \n",
      "\n",
      "531.6117003979502 <= 32057.822633485262  ? \n",
      "\n",
      "Yes.\n"
     ]
    }
   ],
   "source": [
    "# D. Scott\n",
    "# Linear Algebra: TCI\n",
    "# Code Challenge 6.4\n",
    "# Cauchy-Schwarz inequality verification\n",
    "\n",
    "import random\n",
    "import numpy as np\n",
    "\n",
    "A = np.empty((5,9),dtype=int)\n",
    "v = np.empty((1,5),dtype=int)\n",
    "\n",
    "# generate diagonal 6 x 6 matrix\n",
    "for i in range(0,5):\n",
    "    for j in range(0,9):\n",
    "        A[i][j] = random.randint(-4,12)\n",
    "\n",
    "# generate 1 x 5 vector\n",
    "for i in range(0,5):\n",
    "    v[0][i] = random.randint(-4,12)\n",
    "\n",
    "print(\"Matrix A:\\n\",A,\"\\n\")\n",
    "print(\"Vector v:\\n\",v,\"\\n\")\n",
    "\n",
    "print(\"v@A:\\n\",v@A,\"\\n\")\n",
    "print(\"||v@A||\\n\",np.linalg.norm(v@A))\n",
    "\n",
    "F_norm = np.trace(A@A.transpose())\n",
    "print(\"Frobenius norm of A (tr(A@A.T)): \\n\",F_norm)\n",
    "print(\"||v||*||A_f||: \",np.linalg.norm(v)*F_norm,\"\\n\")\n",
    "\n",
    "print(np.linalg.norm(v@A),\"<=\",np.linalg.norm(v)*F_norm,\" ? \\n\")\n",
    "print(\"Yes.\")"
   ]
  }
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