Chapter 32: Some Linear Algebra

Introduction

This chapter contains a review of the basics of linear algebra: the solution of linear equations, matrix inversion, determinants, transformations, invariants, eigenvalues, and diagonalizability.

Topics

32.1   Linear Equations

32.2   Matrices

32.3   The Inverse of a Matrix

32.4   More on Determinants

32.5   Matrices and Transformations

32.6   Invariants of Transformations

32.7   Other Notions of Diagonalizability

32.8   Computing Eigenvalues and Eigenvectors

32.9   Application to Quadratic Forms and Spring Systems

32.10  Computing Eigenvalues and Eigenvectors on a Spreadsheet

32.11  Guessing Eigenvectors