D07 NumPy 的矩陣函式與線性代數應用 作業題目.ipynb

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   "source": [
    "作業目標<br>\n",
    "活用矩陣運算，實做線性代數<br>\n",
    "作業重點<br>\n",
    "線性代數公式應用<br>\n",
    "矩陣相乘維度需要對好，例如:2X3矩陣乘上3X5矩陣得到2X5矩陣"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "題目:<br>\n",
    "array1 = np.array([[10, 8], [3, 5]]) <br>\n",
    "1. 運用上列array計算反矩陣，乘上原矩陣，並觀察是否為單位矩陣?\n",
    "2. 運用上列array計算特徵值、特徵向量?\n",
    "3. 運用上列array計算SVD?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "YakNatIPj3CW"
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "QT4ntMV1kR1c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10,  8],\n",
       "       [ 3,  5]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#1. 運用上列array計算反矩陣，乘上原矩陣，並觀察是否為單位矩陣?\n",
    "array1 = np.array([[10, 8], [3, 5]])\n",
    "array1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.19230769, -0.30769231],\n",
       "       [-0.11538462,  0.38461538]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 計算反矩陣\n",
    "array2 = np.linalg.inv(array1)\n",
    "array2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0.],\n",
       "       [0., 1.]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 乘上原矩陣\n",
    "array3 = np.dot(array1, array2)\n",
    "array3\n",
    "\n",
    "# 是單位矩陣]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "9f7cVxwwk-y9"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1., 1.]),\n",
       " array([[1., 0.],\n",
       "        [0., 1.]]))"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#2. 運用上列array計算特徵值、特徵向量?\n",
    "np.linalg.eig(array3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "id": "OHSs5etxnL8D"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[0., 1.],\n",
       "        [1., 0.]]),\n",
       " array([1., 1.]),\n",
       " array([[0., 1.],\n",
       "        [1., 0.]]))"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#3. 運用上列array計算SVD?\n",
    "np.linalg.svd(array3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "5BaVZFRvpXZo"
   },
   "outputs": [],
   "source": []
  }
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