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1Vector spaces
2Linear maps and matrices
3Linear systems and row reduction
4Dimension
5Determinants
6Inner product spaces
7Eigenvalues and diagonalization
8The spectral theorems
9The singular value decomposition
10Generalized eigenspaces and Jordan form
11Markov chains and positive matrices
12Bilinear and quadratic forms
13Duality and multilinear algebra*
14Linear algebra and abstract algebra*
15Infinite-dimensional vector spaces*
16Applications to data and machine learning*
ASets, functions, and proofs
BComplex numbers
1. Overview
2. B.1Complex numbers
CThe Fundamental Theorem of Algebra*
1. Overview
2. C.1Proofs of the Fundamental Theorem of Algebra

Index of techniques
Practice
PDF

Chapter 14

14Linear algebra and abstract algebra

Beyond 21-242 This chapter goes beyond the course.

Groups through matrices, field extensions, finite fields, and modules over F[x] with rational canonical form.

In this chapter

14.1Groups through matrices
14.2Fields and field extensions
14.3Finite fields
14.4Modules over F[x] and canonical forms
14.5Proof patterns

Previous13.5Proof patterns Next14.1Groups through matrices