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    "---\n",
    "title: Biostat 216 Homework 3\n",
    "subtitle: 'Due Oct 18 @ 11:59pm'\n",
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    "Submit a PDF (scanned/photographed from handwritten solutions, or converted from RMarkdown or Jupyter Notebook or Quarto) to Gradescope in BruinLearn. \n",
    "\n",
    "## Q1. Computational complexity of matrix multiplication\n",
    "\n",
    "Let $\\mathbf{A} \\in \\mathbb{R}^{m \\times n}$, $\\mathbf{B} \\in \\mathbb{R}^{n \\times p}$. Consider four ways of computing the matrix product $\\mathbf{C} = \\mathbf{A} \\mathbf{B}$. Calculate the flop count (leading term) in each of these four algorithms.\n",
    "\n",
    "1. (Inner products) Evaluate entries $c_{ij} = \\mathbf{a}_i' \\mathbf{b}_j$ for all $i, j$.\n",
    "\n",
    "2. (Matrix vector products) Evaluate columns $\\mathbf{c}_j = \\mathbf{A} \\mathbf{b}_j$ for all $j$.\n",
    "\n",
    "3. (Vector matrix products) Evaluate rows $\\mathbf{c}_i' = \\mathbf{a}_i' \\mathbf{B}$ for all $i$.\n",
    "\n",
    "4. (Vector outer products) Evaluate $\\mathbf{C}$ as the sum of outer prodcuts $\\mathbf{a}_1 \\mathbf{b}_1' + \\cdots + \\mathbf{a}_n \\mathbf{b}_n'$."
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    "## BV exercises\n",
    "\n",
    "7.12, 7.13, 7.14, 8.4, 8.5, 8.6, 8.9, 10.9 (also describe $\\mathbf{C}=\\mathbf{A} \\mathbf{D}$), 10.11, 10.19, 10.23, 10.36, 10.42, 10.43, 10.44"
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