Mathematical Foundations · Linear Algebra

Advanced Linear Algebra: Euclidean Spaces, Orthogonality, Projection and Least Squares

Public introduction · full guide in Eikos

Introduction

What this guide covers

A rigorous study on the metric structures of vector spaces, the geometric design of projection operators and the quadratic optimization of overterminated systems.

Overview

Topics covered

  • Introduction
  • Euclidean Spaces, Orthogonality, Projections and Least Squares
  • Euclidean Space and Metric Structure
  • 1.1 Axiomatic Definition of an Internal Product
  • The Canonical Scalar Product in
  • Generalized Internal Products through Matrices

Related concepts

Main connections

  • Linear algebra & matrices
  • Linear regression
  • Variance & standard deviation
  • Conditional probability & independence
  • Calculus & differentiation
  • Skewness & kurtosis

Compatible notation

Mathematical sample in LaTeX

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

⟨⋅,⋅⟩:V×V⟶ℝ
View LaTeX source\langle \cdot, \cdot \rangle : V \times V \longrightarrow \mathbb{R}