Mathematical Foundations · Linear Algebra

Treatise on Linear Algebra: Linear Applications

Public introduction · full guide in Eikos

Introduction

What this guide covers

A comprehensive and rigorous analysis of homomorphisms between vector spaces, their matrix representations, base change, spectral decomposition, duality and their advanced applications in numerical methods and computer graphics.

Overview

Topics covered

  • Introduction
  • Linear Algebra: Linear Applications
  • Concept and Definition of Linear Application
  • Immediate Properties of Linear Applications
  • Examples and Inexamples of Linearity
  • Core and Image of a Linear Application

Related concepts

Main connections

  • Linear algebra & matrices
  • Principal component analysis (PCA)
  • Conditional probability & independence
  • Supervised machine learning
  • Calculus & differentiation
  • Variance & standard deviation

Compatible notation

Mathematical sample in LaTeX

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

f(u+v)=f(u)+f(v)∀u,v∈V
View LaTeX sourcef(u + v) = f(u) + f(v) \quad \forall u, v \in V