{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f82ee212-d46c-43bb-a0d1-a68f3cd1dfa6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5×5 Matrix{Float64}:\n",
       "  1.87346    0.927913   2.52746   -0.482284   0.513368\n",
       "  0.927913   3.18765    0.958831  -0.350004   2.53703\n",
       "  2.52746    0.958831   5.76174   -0.179455  -0.781054\n",
       " -0.482284  -0.350004  -0.179455   1.03152    0.015535\n",
       "  0.513368   2.53703   -0.781054   0.015535   5.93971"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "5×1 Matrix{Float64}:\n",
       " -1.6078855163050978\n",
       " -0.23218159505096736\n",
       " -0.6715758819689612\n",
       " -2.3296877597548655\n",
       "  1.2016661898413077"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using LinearAlgebra\n",
    "\n",
    "A = randn(5,5)\n",
    "Q = A' * A # positive definite\n",
    "\n",
    "v = randn(5,1)\n",
    "\n",
    "display(Q)\n",
    "display(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "74a7b8e6-03b2-4799-abd2-6cdb7a644259",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5-element Vector{Float64}:\n",
       " -4.9930629530914805\n",
       " -0.8132084512107426\n",
       "  2.243541240545553\n",
       " -4.498023206367981\n",
       "  1.2879883872115698"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using IterativeSolvers\n",
    "\n",
    "cg(Q, v) # next lesson for the real one"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.9.3",
   "language": "julia",
   "name": "julia-1.9"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.9.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}