Mat/Wrzodak_Koszarek_Zadania.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Zadanie 4.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sympy import symbols, Matrix\n",
    "from numpy.linalg import eig\n",
    "\n",
    "A=np.matrix(QQ,5,3,[2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 31])\n",
    "print(A.transpose()*A)\n",
    "print((A.transpose()*A)^(-1))\n",
    "mm=(A.transpose()*A)^(-1)\n",
    "mm=(A.transpose()*A)^(-1)*A.transpose()\n",
    "print(mm)\n",
    "\n",
    "b1=np.vector([-1,0,1,0,1])\n",
    "mm1=mm*b1\n",
    "print(mm1)\n",
    "print((b1-A*mm1))\n",
    "b2=np.vector([1,1,1,1,1])\n",
    "mm2=mm*b2\n",
    "print(mm2)\n",
    "print((b2-A*mm2))\n",
    "\n",
    "b2 in (m.transpose()).image()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zadanie 4.7\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "zb1=[(1,1),(2,3),(4,5)]\n",
    "zb2=[(1,1),(2,3),(3,4),(4,5),(5,7),(6,9)]\n",
    "\n",
    "m1=matrix(3,2,[1,exp(1.0),1,exp(2.0),1,exp(4.0)])\n",
    "m2=matrix(6,2,[1,exp(1.0),1,exp(2.0),1,exp(3.0),1,exp(4.0),1,exp(5.0),1,exp(6.0)])\n",
    "\n",
    "a,b,t=var('a,b,t')\n",
    "\n",
    "m1*vector([a,b])-vector([1,3,5])\n",
    "m2*vector([a,b])-vector([1,3,4,5,7,9])\n",
    "\n",
    "\n",
    "\n",
    "M1=m1.transpose()*m1\n",
    "M1.det()\n",
    "\n",
    "\n",
    "\n",
    "M2=m2.transpose()*m2\n",
    "M2.det()\n",
    "\n",
    "\n",
    "\n",
    "M1^(-1)*m1.transpose()*vector([1,3,5])\n",
    "\n",
    "M2^(-1)*m2.transpose()*vector([1,3,4,5,7,9])\n",
    "\n",
    "\n",
    "plot(1.64148598265947+ 0.0629860338045423*exp(t),(t,0,4))+sum([point(x) for x in zb1])\n",
    "\n",
    "plot(3.10041190358990+ 0.0163320609303546*exp(t),(t,0,6))+sum([point(x) for x in zb2])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zadanie 4.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "m=matrix(3,3,[1,1,0,1,2,2,0,2,3])\n",
    "\n",
    "eigenvalues = np.m.eigvals(matrix)\n",
    "\n",
    "eigen=m.right_eigenvectors()\n",
    "e1=eigen[0][1][0]\n",
    "e2=eigen[1][1][0]\n",
    "print(e1.dot_product(e2))\n",
    "e3=eigen[2][1][0]\n",
    "print(e3.dot_product(e1))\n",
    "print(e2.dot_product(e3))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "name": "python",
   "version": "3.10.9"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}