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   "source": [
    "## Ejemplo 5.1: Producto de Krönecker"
   ]
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    "$\\newcommand{\\ket}[1]{|{#1}\\rangle}\\newcommand{\\bra}[1]{\\langle{#1}|}$\n",
    "Si $\\boldsymbol{A}$ y $\\boldsymbol{B}$ son dos matrices de dimensión $2\\times 2$ se tiene que\n",
    "\\begin{align*}\n",
    "\\boldsymbol{A} \\otimes \\boldsymbol{B} =\n",
    "\\begin{bmatrix}\n",
    "a_{11} & a_{12} \\\\\n",
    "a_{21} & a_{22}\n",
    "\\end{bmatrix}\n",
    "\\otimes\n",
    "\\begin{bmatrix}\n",
    "b_{11} & b_{12}\\\\\n",
    "b_{21} & b_{22}\n",
    "\\end{bmatrix} =\n",
    "\\begin{bmatrix}\n",
    "a_{11} b_{11} & a_{11} b_{12} & a_{12} b_{11} & a_{12} b_{12} \\\\\n",
    "a_{11} b_{21} & a_{11} b_{22} & a_{12} b_{21} & a_{12} b_{22} \\\\\n",
    "a_{21} b_{11} & a_{21} b_{12} & a_{22} b_{11} & a_{22} b_{12} \\\\\n",
    "a_{21} b_{21} & a_{21} b_{22} & a_{22} b_{21} & a_{22} b_{22}\n",
    "\\end{bmatrix}.\n",
    "\\end{align*}\n"
   ]
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     "text": [
      "A =\n",
      " [[0 1]\n",
      " [2 3]] \n",
      "B =\n",
      " [[10 11]\n",
      " [12 13]] \n",
      "A ⊗ B =\n",
      " [[ 0  0 10 11]\n",
      " [ 0  0 12 13]\n",
      " [20 22 30 33]\n",
      " [24 26 36 39]]\n"
     ]
    }
   ],
   "source": [
    "# El comando de numpy que realiza el producto de Kroenecker es kron(A,B):\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "A = np.array([[0, 1], [2, 3]])\n",
    "B = np.array([[10, 11], [12, 13]])\n",
    "A_kron_B = np.kron(A, B)\n",
    "\n",
    "print(\"A =\\n\", str(A), \"\\nB =\\n\", str(B), \"\\nA ⊗ B =\\n\", str(A_kron_B))\n"
   ]
  }
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