Mathematical Foundations · Linear Algebra

Advanced Linear Algebra · Bilinear and Quadratic Forms

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Introduction Advanced Linear Algebra · Metric geometry

Overview

Topics covered

  • Introduction
  • Bilinear and quadratic forms
  • Preliminaries: duality, linear forms and the tensor product
  • The tensor structure of multilinear applications
  • Bilinear forms: definition, matrix representation and change of base
  • The matrix representation

Related concepts

Main connections

  • Linear algebra & matrices
  • Supervised machine learning
  • Calculus & differentiation
  • Mathematical optimization & gradients

Compatible notation

Mathematical sample in LaTeX

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

V*=Hom𝕂(V,𝕂)={f:V→𝕂∣fIt is linear}
View LaTeX sourceV^* = \Hom_\K(V, \K) = \{ f: V \to \K \mid f \text{It is linear} \}