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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Homework \\#1 template"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 8x8 Haar matrix\n",
    "H = np.array([\n",
    "    [1, -1,  0,  0,  0,  0,  0,  0],\n",
    "    [0,  0,  1, -1,  0,  0,  0,  0],\n",
    "    [0,  0,  0,  0,  1, -1,  0,  0],\n",
    "    [0,  0,  0,  0,  0,  0,  1, -1],\n",
    "    [1,  1, -1, -1,  0,  0,  0,  0],\n",
    "    [0,  0,  0,  0,  1,  1, -1, -1],\n",
    "    [1,  1,  1,  1, -1, -1, -1, -1],\n",
    "    [1,  1,  1,  1,  1,  1,  1,  1]\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# b) show that the rows are linearly independent\n",
    "# ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# c) verify that HH^T is symmetric\n",
    "# ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# d) compute a basis expansion\n",
    "x = np.ones((8,1)) # note that we specify the shape to obtain a column vector\n",
    "\n",
    "# ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# e) compute a basis expansion\n",
    "y = ..."
   ]
  }
 ],
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