Linear Algebra is a text for a first US undergraduate Linear Algebra course. You can use it as a main text, as a supplement, or for independent study. The topics covered include: linear systems and Gauss's method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues.
This book covers the requisite material and proves all the results, but it does not assume that students are proficient at abstract work. Instead, it proceeds with a great deal of motivation, many computational examples and exercises that range from routine verifications to a few challenges. The goal is, in the context of developing the material of an undergraduate course, to raise each student's level of mathematical maturity.
Each chapter finishes with four or five short supplemental topics. These are good for reading or projects, or for small group work. Each subsection has many exercises spanning a range of difficulty. In the Answers book each exercise is covered, completely, including proofs.
Prerequisite: One semester of calculus.
Conditions of Use
This book is licensed under a Creative Commons License (CC BY-NC-SA). You can download the ebook Linear Algebra, 4th Edition for free.
- Title
- Linear Algebra, 4th Edition
- Publisher
- OpenIntro
- Author(s)
- Jim Hefferon
- Published
- 2021-06-06
- Edition
- 4
- Format
- eBook (pdf, epub, mobi)
- Pages
- 526
- Language
- English
- ISBN-10
- 1944325115
- ISBN-13
- 9781944325114
- License
- CC BY-NC-SA
- Book Homepage
- Free eBook, Errata, Code, Solutions, etc.
Linear Systems Solving Linear Systems Gauss's Method Describing the Solution Set General=Particular+Homogeneous Linear Geometry Vectors in Space Length and Angle Measures Reduced Echelon Form Gauss-Jordan Reduction The Linear Combination Lemma Topic: Computer Algebra Systems Topic: Input-Output Analysis Topic: Accuracy of Computations Topic: Analyzing Networks Vector Spaces Definition of Vector Space Definition and Examples Subspaces and Spanning Sets Linear Independence Definition and Examples Basis and Dimension Basis Dimension Vector Spaces and Linear Systems Combining Subspaces Topic: Fields Topic: Crystals Topic: Voting Paradoxes Topic: Dimensional Analysis Maps Between Spaces Isomorphisms Definition and Examples Dimension Characterizes Isomorphism Homomorphisms Definition Range Space and Null Space Computing Linear Maps Representing Linear Maps with Matrices Any Matrix Represents a Linear Map Matrix Operations Sums and Scalar Products Matrix Multiplication Mechanics of Matrix Multiplication Inverses Change of Basis Changing Representations of Vectors Changing Map Representations Projection Orthogonal Projection Into a Line Gram-Schmidt Orthogonalization Projection Into a Subspace Topic: Line of Best Fit Topic: Geometry of Linear Maps Topic: Magic Squares Topic: Markov Chains Topic: Orthonormal Matrices Determinants Definition Exploration Properties of Determinants The Permutation Expansion Determinants Exist Geometry of Determinants Determinants as Size Functions Laplace's Formula Laplace's Expansion Topic: Cramer's Rule Topic: Speed of Calculating Determinants Topic: Chiò's Method Topic: Projective Geometry Topic: Computer Graphics Similarity Complex Vector Spaces Polynomial Factoring and Complex Numbers Complex Representations Similarity Definition and Examples Diagonalizability Eigenvalues and Eigenvectors Nilpotence Self-Composition Strings Jordan Form Polynomials of Maps and Matrices Jordan Canonical Form Topic: Method of Powers Topic: Stable Populations Topic: Page Ranking Topic: Linear Recurrences Topic: Coupled Oscillators Appendix Statements Quantifiers Techniques of Proof Sets, Functions, and Relations
