Looking for linear algebra books? We've gathered 15 free linear algebra books in PDF, covering topics like vector spaces, matrices, eigenvalues, linear transformations, determinants, and systems of equations.
These books range from beginner-friendly introductions to rigorous textbooks used in top universities. Authors like Sheldon Axler, Jim Hefferon, and David Cherney have made their work freely available.
Browse our top picks or explore by level. Every book is free to read online or download as PDF.
Introductory Linear Algebra Books
Taking your first linear algebra course? These books cover systems of equations, matrices, and vector spaces from the ground up.
Covers systems of equations, vectors, matrices, determinants, eigenvalues, and linear transformations with detailed examples and exercises. Ideal for building a strong foundation in linear algebra.
A well-structured introduction to linear algebra for science and engineering students. Covers all major topics with proofs of important theorems and numerous exercises.
An engaging undergraduate textbook that starts with organizing information and builds through systems of equations, vector spaces, eigenvalues, and the simplex method.
David Cherney, Tom Denton, Rohit Thomas, Andrew Waldron
Develops linear algebra from linear equations and matrices through vector spaces, fields, determinants, eigenvalues, and canonical forms. Includes LU and LPDU factorization.
These are the standard college-level textbooks used in universities worldwide. They cover vector spaces, linear transformations, eigenvalues, and determinants with proofs and exercises.
A best-selling textbook that takes an innovative approach by avoiding determinants until the end. Covers vector spaces, linear maps, eigenvalues, inner product spaces, and operators on complex vector spaces.
A developmental textbook that builds mathematical maturity through Gaussian reduction, vector spaces, linear maps, determinants, and eigenvalues. Features extensive examples and motivation.
An honors-level textbook designed for mathematically advanced students. Emphasizes topics important for analysis, geometry, and probability while building skills in rigorous proof writing.
An open educational resource covering linear systems, vector spaces, linear transformations, determinants, eigenvalues, and inner product spaces with clear explanations and exercises.
Linear algebra is the backbone of data science, engineering, and machine learning. These books focus on real-world applications like least squares, data fitting, and computational methods.
Focuses on vectors, matrices, and least squares with real-world applications including clustering, data fitting, and classification. Used at Stanford and other top universities.
Balances theory with practical applications across linear equations, matrix algebra, determinants, vector spaces, eigenvalues, orthogonality, and singular value decomposition.
Written for non-mathematicians who need linear algebra for physics and engineering. Covers vector spaces, matrices, and applications with accessible explanations and practical examples.
A comprehensive treatment of linear algebra with applications to computer vision, robotics, and machine learning. Covers SVD, spectral theory, Haar wavelets, and optimization methods.
Ready for graduate-level material? These books tackle spectral theory, Jordan canonical form, and abstract vector spaces for readers with a solid foundation.
Bridges linear algebra and abstract mathematics through complex numbers, vector spaces, inner products, and the spectral theorem. Builds skills for proof-based mathematics courses.
Isaiah Lankham, Bruno Nachtergaele, Anne Schilling
A concise treatment of groups, rings, fields, and linear algebra emphasizing matrix theory and proofs. Designed as a foundation for both mathematics and computer science students.
Covers numerical linear algebra including orthogonality, SVD, solving linear systems, and the algebraic eigenvalue problem. Interweaves theory with programming activities and videos.
Linear algebra is one of the most useful branches of mathematics. Whether you need it for a college course, a career in tech, or pure curiosity, these books have you covered.
