'matrix problems'

Author: DPotoyan

ch03/demo_operators.ipynb

@@ -9,12 +9,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [],
    "source": [
     "import numpy as np\n",
     "import matplotlib.pyplot as plt\n",
+    "from ipywidgets import widgets\n",
     "from ipywidgets.widgets import interact, interactive\n",
     "\n",
     "%matplotlib inline\n",
@@ -30,7 +31,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -61,9 +62,34 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 3,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "39110dcd05c146da84f09e1e72557dc1",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "interactive(children=(IntSlider(value=0, description='x', max=10, min=-10), IntSlider(value=0, description='y'…"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "<function __main__.plot_vector(x, y)>"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "def plot_vector(x, y):\n",
     "\n",
@@ -91,7 +117,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -112,16 +138,34 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 8,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "175112b533e3462e956b0409b0cc3002",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "interactive(children=(IntSlider(value=1, description='a', max=5, min=-5), IntSlider(value=0, description='b', …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "<function __main__.matrix_transform(a=1, b=0, c=0, d=1)>"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "def matrix_transform(a=1, b=0, c=0, d=1):\n",
     "    matrix = np.array([[a, b], [c, d]])\n",
@@ -152,6 +196,82 @@
     "                 d=widgets.IntSlider(min=-5, max=5, value=1, description=\"d\"))\n"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Solve linear euqation by matrix inversion"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Solution using matrix inversion:\n",
+      "x = [2.42857143 0.71428571]\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Define the coefficients matrix A and the right-hand side vector b\n",
+    "A = np.array([[2, 3],\n",
+    "              [1, -2]])\n",
+    "\n",
+    "b = np.array([7, 1])\n",
+    "\n",
+    "# Calculate the inverse of matrix A\n",
+    "A_inv = np.linalg.inv(A)\n",
+    "\n",
+    "# Solve for the unknown vector x using matrix inversion: x = A_inv * b\n",
+    "x = np.dot(A_inv, b)\n",
+    "\n",
+    "print(\"Solution using matrix inversion:\")\n",
+    "print(\"x =\", x)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Compute eigenvalues and eigenvectors"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "eigvals:\n",
+      "[-0.5+0.8660254j -0.5-0.8660254j]\n",
+      "eigvecs:\n",
+      "[[0.8660254+0.j   0.8660254-0.j  ]\n",
+      " [0.4330127-0.25j 0.4330127+0.25j]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Define the coefficients matrix A and the right-hand side vector b\n",
+    "# vary coeficients\n",
+    "A = np.array([[1, -3],\n",
+    "              [1, -2]])\n",
+    "\n",
+    "# Calculate the eigenvalues and eigenvectors of A\n",
+    "eigenvalues, eigenvectors = np.linalg.eig(A)\n",
+    "print('eigvals:')\n",
+    "print(eigenvalues)\n",
+    "print('eigvecs:')\n",
+    "print(eigenvectors)"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,