Digital library
Textbooks, references and open learning resources.
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Linear Algebra Done Right
Sheldon Axler · Springer · 2024
Now available in Open Access, this best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate students. The fourth edition gives an expanded treatment of the singular value decomposition and its consequences. It includes a new chapter on multilinear algebra, treating bilinear forms, quadratic forms, tensor products, and an approach to determinants via alternating multilinear forms. This new edition also increases the use of the minimal polynomial to provide cleaner proofs of multiple results. Also, over 250 new exercises have been added. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. Beautiful formatting creates pages with an unusually student-friendly appearance in both print and electronic versions. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. The text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.
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Introduction to GNU Octave: A brief tutorial for linear algebra and calculus students
Jason Lachniet · Jason Lachniet · 2017
This brief book provides a noncomprehensive introduction to GNU Octave, a free open source alternative to MatLab. The basic syntax and usage is explained through concrete examples from the mathematics courses a math, computer science, or engineering major encounters in the first two years of college: linear algebra, calculus, and differential equations.
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Linear Algebra with Applications
W. Keith Nicholson · Lyryx · 2023
The aim of this textbook is to achieve a balance among computational skills, theory, and applications of linear algebra. It is a relatively advanced introduction to the ideas and techniques of linear algebra targeted for science and engineering students who need to understand not only how to use these methods but also gain insight into why they work. The content has enough flexibility to present a traditional introduction to the subject, or to allow for a more applied course. Chapters 1–4 contain a one-semester course for beginners, whereas Chapters 5–9 contain a second semester course. The textbook is primarily about real linear algebra with complex numbers being mentioned when appropriate (reviewed in Appendix A).
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A First Course in Linear Algebra
Ken Kuttler · Lyryx · 2023
This text, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course in linear algebra for science and engineering students who have an understanding of basic algebra. All major topics of linear algebra are available in detail, as well as proofs of important theorems. In addition, connections to topics covered in advanced courses are introduced. The text is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile. Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the text. Lyryx develops and supports open texts, with editorial services to adapt the text for each particular course. In addition, Lyryx provides content-specific formative online assessment, a wide variety of supplements, and in-house support available 7 days/week for both students and instructors.
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Linear Algebra, Theory And Applications
Kenneth Kuttler · Saylor Foundation · 2012
This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however. This book features an ugly, elementary, and complete treatment of determinants early in the book. Thus it might be considered as Linear algebra done wrong. I have done this because of the usefulness of determinants. However, all major topics are also presented in an alternative manner which is independent of determinants. The book has an introduction to various numerical methods used in linear algebra. This is done because of the interesting nature of these methods. The presentation here emphasizes the reasons why they work. It does not discuss many important numerical considerations necessary to use the methods effectively. These considerations are found in numerical analysis texts.
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Linear Algebra
David Cherney; Tom Denton; Andrew Waldon · University of California, Davis · 2016
We believe the entire book can be taught in twenty five 50-minute lectures to a sophomore audience that has been exposed to a one year calculus course. Vector calculus is useful, but not necessary preparation for this book, which attempts to be self-contained. Key concepts are presented multiple times, throughout the book, often first in a more intuitive setting, and then again in a definition, theorem, proof style later on. We do not aim for students to become agile mathematical proof writers, but we do expect them to be able to show and explain why key results hold. We also often use the review exercises to let students discover key results for themselves; before they are presented again in detail later in the book. The book has been written such that instructors can reorder the chapters (using the La- TeX source) in any (reasonable) order and still have a consistent text. We hammer the notions of abstract vectors and linear transformations hard and early, while at the same time giving students the basic matrix skills necessary to perform computations. Gaussian elimination is followed directly by an “exploration chapter” on the simplex algorithm to open students minds to problems beyond standard linear systems ones. Vectors in Rn and general vector spaces are presented back to back so that students are not stranded with the idea that vectors are just ordered lists of numbers. To this end, we also labor the notion of all functions from a set to the real numbers. In the same vein linear transformations and matrices are presented hand in hand. Once students see that a linear map is specified by its action on a limited set of inputs, they can already understand what a basis is. All the while students are studying linear systems and their solution sets, so after matrices determinants are introduced. This material can proceed rapidly since elementary matrices were already introduced with Gaussian elimination. Only then is a careful discussion of spans, linear independen
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Linear Algebra
Jim Hefferon · Jim Hefferon · 2016
This text covers the standard material for a US undergraduate first course: linear systems and Gauss's Method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues, as well as additional topics such as introductions to various applications. It has extensive exercise sets with worked answers to all exercises, including proofs, beamer slides for classroom use, and a lab manual for computer work. The approach is developmental. Although everything is proved, it introduces the material with a great deal of motivation, many computational examples, and exercises that range from routine verifications to a few challenges. Ancillary materials are available at the publisher link.
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A First Course in Linear Algebra
Robert Beezer · Robert Beezer · 2015
A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically students will have taken calculus, but it is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Determinants and eigenvalues are covered along the way. A unique feature of this book is that chapters, sections and theorems are labeled rather than numbered. For example, the chapter on vectors is labeled "Chapter V" and the theorem that elementary matrices are nonsingular is labeled "Theorem EMN." Another feature of this book is that it is designed to integrate SAGE, an open source alternative to mathematics software such as Matlab and Maple. The author includes a 45-minute video tutorial on SAGE and teaching linear algebra. This textbook has been used in classes at: Centre for Excellence in Basic Sciences, Westmont College, University of Ottawa, Plymouth State University, University of Puget Sound, University of Notre Dame, Carleton University, Amherst College, Felician College, Southern Connecticut State University, Michigan Technological University, Mount Saint Mary College, University of Western Australia, Moorpark College, Pacific University, Colorado State University, Smith College, Wilbur Wright College, Central Washington U (Lynwood Center), St. Cloud State University, Miramar College, Loyola Marymount University.
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Scientific Computing
Jeffrey R. Chasnov · Hong Kong University of Science and Technology
In the contents: 5: Linear Algebra
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Engineering Modeling and Analysis with Python, 2E
Carl Greco, Zahra Zamanipour and Thomas Dodds · Arkansas Tech University
An open-access textbook designed to equip undergraduate engineering students with core computational and analytical skills using the Python ecosystem. It transitions from fundamental Python programming concepts, such as data structures, control flow, file I/O, and object-oriented programming into practical applications with libraries like NumPy, SciPy, Matplotlib, Pandas, and SymPy. Dynamic systems, solve linear algebra equations, and visualize engineering data.
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Applied Geometric Algebra (Tisza)
László Tisza · Massachusetts Institute of Technology
In the contents: 01: Algebraic Preliminaries · 1.05: A short survey of linear groups · 02: The Lorentz Group and the Pauli Algebra
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Computational Physics
Y. D. Chong · Nanyang Technological University
In the contents: 04: Numerical Linear Algebra · 4.02: Linear Equations · 8.01: Sparse Matrix Algebra
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Math 091: Essentials of Intermediate Algebra
Patrick Kwon · Highline College
In the contents: 02: Linear Equations · 2.01: Linear Functions - Applications · 2.02: Prelude to Solving Linear Equations
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MTH 65: Algebra 2
Math Department · Clackamas Community College
TThis book builds a strong algebra foundation. You’ll review core skills like order of operations, fractions, and linear equations, then expand into polynomials, exponents, roots, and radicals. Finally, you’ll explore absolute value to model distance, tolerance, and precision. These connected skills form a toolkit to solve problems confidently and prepare you for advanced math and real-world applications.
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Matrix Analysis
Steve Cox · Rice University
Equilibria and the solution of linear and linear least squares problems. Dynamical systems and the eigenvalue problem with the Jordan form and Laplace transform via complex integration.
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Matrix Algebra with Computational Applications
Dirk Colbry · Michigan State University
In the contents: 01: Matrix Algebra class preparation checklist · 02: 01 In-Class Assignment - Welcome to Matrix Algebra with computational applications · 4.1: Example linear system
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All Things Flow - Fluid Mechanics for the Natural Sciences
Bill Smyth · Oregon State University
In the contents: 02: Review of Elementary Linear Algebra · 2.03: Systems of linear equations · 09: Nonlinear, Hydrostatic Flow Over Topography
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Math 111: College Algebra
Highline College
In the contents: 1.04: Linear Functions · 1.4.01: Linear Functions (Exercises) · 1.05: Graphs of Linear Functions
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MTH 95: Algebra 3
Math Department · Clackamas Community College
In the contents: 01: Linear Relationships Equations and Inequalities · 1.02: Linear Models and Rates of Change · 1.03: Linear Equations and Systems
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Applied Geometric Algebra
László Tisza · Massachusetts Institute of Technology
In the contents: 02: Algebraic Preliminaries · 2.05: A short survey of linear groups · 03: The Lorentz Group and the Pauli Algebra