commit

Author: TarrySingh

Beginners_Guide_Math_LinAlg/Math/Abstract Algebra/Matrix Algebra.ipynb

@@ -0,0 +1,59 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Here are a few definitions and basic properties of matrices. \n",
+    "\n",
+    "Those who are not yet familiar with these terms can simply assume that the entries are real numbers.\n",
+    "\n",
+    "Let $R$ be a ring and $m$ and $n$ positive integers. Then an $m \\times n$ matrix over $R$ is an array of elements of $R$ with $m$ rows and $n$ columns. If our matrix is $A$ then we write $a_{i j}$ for the $(i, j)$ -entry of $A$; that is,\n",
+    "$$\n",
+    "A=\\left(\\begin{array}{cccc}\n",
+    "a_{11} & a_{12} & \\cdots & a_{1 n} \\\\\n",
+    "a_{21} & a_{22} & \\cdots & a_{2 n} \\\\\n",
+    "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
+    "a_{m 1} & a_{m 2} & \\cdots & a_{m n}\n",
+    "\\end{array}\\right)\n",
+    "$$\n",
+    "Example B.I. If we let\n",
+    "$$\n",
+    "A=\\left(\\begin{array}{lll}\n",
+    "4 & 6 & 7 \\\\\n",
+    "3 & 8 & 5\n",
+    "\\end{array}\\right)\n",
+    "$$\n",
+    "then $A$ is a $2 \\times 3$ matrix over $\\mathbb{R}$. Furthermore, $a_{12}=6$ and $a_{21}=3$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.4"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

Beginners_Guide_Math_LinAlg/Math/Abstract Algebra/Sets and Operations.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "A *set* is a collection of objects. We will see many sorts of sets throughout this notebook series. Perhaps the most common will be sets of numbers. For instance, we have the set of *natural numbers*\n",
+    "\n",
+    "$$\n",
+    "\\mathbb{N}=\\{1,2,3, \\ldots\\}\n",
+    ",$$\n",
+    "\n",
+    "the set of *integers*,\n",
+    "\n",
+    "$$\n",
+    "\\mathbb{Z}=\\{\\ldots,-2,-1,0,1,2, \\ldots\\}\n",
+    "$$\n",
+    "and the set of *rational numbers*\n",
+    "\n",
+    "$$\n",
+    "\\mathbb{Q}=\\left\\{\\frac{a}{b}: a, b \\in \\mathbb{Z}, b \\neq 0\\right\\}\n",
+    ".$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.4"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

Beginners_Guide_Math_LinAlg/Math/Eigenvalue Computation.ipynb

@@ -50,7 +50,7 @@
   },
   {
    "cell_type": "code",
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+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
@@ -75,7 +75,7 @@
   },
   {
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+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
@@ -96,7 +96,7 @@
   },
   {
    "cell_type": "code",
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+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
@@ -115,7 +115,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -164,7 +164,7 @@
   },
   {
    "cell_type": "code",
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+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {
@@ -245,7 +245,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [
     {
@@ -254,8 +254,8 @@
      "text": [
       "[[ 2.23964345e+01  1.01162895e+00 -3.99289689e+00 -8.64584027e-01]\n",
       " [-9.53185822e-02 -1.31317710e+01  5.71184329e+00  1.95731776e+00]\n",
-      " [ 4.56904318e-16 -2.49934586e-08 -1.67305884e+00 -7.92295866e-01]\n",
-      " [ 1.34398419e-15 -5.60119902e-16 -2.75027919e-05 -5.91604624e-01]]\n"
+      " [ 7.98356699e-17 -2.49934586e-08 -1.67305884e+00 -7.92295866e-01]\n",
+      " [ 1.05756546e-15 -3.55793109e-16 -2.75027919e-05 -5.91604624e-01]]\n"
      ]
     }
    ],
@@ -265,7 +265,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
@@ -306,7 +306,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.4"
+   "version": "3.7.4"
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github/Practicing writing stuff I like -- ANN, Information-Theory, Capsules and more.ipynb

@@ -130,7 +130,7 @@
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    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.1"
+   "version": "3.7.4"
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