Linear-Algebra-Numpy-Examples.ipynb

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   "source": [
    "## Linear Algebra and Numpy\n",
    "Examples taken from \"An Introduction to Data Analysis through a Geometric Lens\" (copyright: Jeff M. Phillips)"
   ]
  },
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   "cell_type": "code",
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   "source": [
    "import numpy as np\n",
    "from numpy import linalg as LA"
   ]
  },
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   "source": [
    "#create an array, a row vector\n",
    "v = np.array([1,2,7,5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "v"
   ]
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   "source": [
    "v[2]"
   ]
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   "source": [
    "#create a n=2 x d=3 matrix\n",
    "A = np.array([[3,4,3],[1,6,7]])"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
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   "outputs": [],
   "source": [
    "A"
   ]
  },
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   "cell_type": "code",
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   "outputs": [],
   "source": [
    "# matrix entry at specified position\n",
    "A[1,2]"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#restrict A to a given range of rows and columns\n",
    "A[:, 1:3]"
   ]
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   "source": [
    "#adding and multiplying vectors\n",
    "u = np.array([3,4,2,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#elementwise add\n",
    "v+u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#elementwise multiply\n",
    "v*u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# dot product\n",
    "v.dot(u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.dot(u,v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#matrix multiplication\n",
    "B = np.array([[1,2],[6,5],[3,4]])\n",
    "A.dot(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "x = np.array([3,4])"
   ]
  },
  {
   "cell_type": "code",
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   "metadata": {},
   "outputs": [],
   "source": [
    "B.dot(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "LA.norm(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Other norms: L1\n",
    "LA.norm(v,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#transpose\n",
    "A.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# vectors always print in row format\n",
    "x.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# vectors always print in row format\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "LA.matrix_rank(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "C = np.array([[1,2],[3,5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "LA.inv(C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "C.dot(LA.inv(C))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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