Mathematical Foundations · Linear Algebra

Advanced Linear Algebra · Diagonalization, Eigenvalues and Eigenvectors

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Chart from the original guide

Overview

Topics covered

  • Introduction
  • Diagonalization and Eigenvalue Theory
  • Historical perspective and geometric motivation
  • The geometric intuition of linear transformation
  • Foundation in Vector Spaces and Operators
  • Effect of a change of coordinates

Related concepts

Main connections

  • Linear algebra & matrices
  • Variance & standard deviation
  • Principal component analysis (PCA)
  • Supervised machine learning
  • Calculus & differentiation
  • Bayes' theorem & priors

Compatible notation

Mathematical sample in LaTeX

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

T∈ℒ(V)⟷[T]ℬ∈𝕂n×n
View LaTeX sourceT \in \mathcal{L}(V) \quad \longleftrightarrow \quad [T]_{\mathcal{B}} \in \mathbb{K}^{n \times n}