Mathematical Foundations · Linear Algebra

Advanced Linear Algebra: Matrices, Determinants and Systems of Linear Equations

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Introduction Introduction Chart from the original guide

Overview

Topics covered

  • Introduction
  • Multidimensional Linear Algebra
  • Matrix spaces and operator algebra
  • Algebraic properties of multiplication
  • The transposition operator and the trace
  • Partitioned or block arrays

Related concepts

Main connections

  • Linear algebra & matrices
  • Permutation & exact tests
  • Linear regression
  • Calculus & differentiation
  • Normal (Gaussian) distribution
  • Supervised machine learning

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

(A+B)ij=aij+bij,(αA)ij=αaij
View LaTeX source(A + B)_{ij} = a_{ij} + b_{ij}, \qquad (\alpha A)_{ij} = \alpha a_{ij}