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50+ Linear Algebra Free Books


"Linear algebra" is generally classified into two main categories: "theoretical linear algebra" and "applied linear algebra". Both areas are deeply connected but serve different purposes. "Theoretical linear algebra" focuses on understanding abstract concepts like "vector spaces", "basis", "dimension", "eigenvalues", and "eigenvectors". It provides a framework for exploring how transformations work and why certain systems behave the way they do. This branch is essential for developing a deeper appreciation of mathematical theory and proofs. "Applied linear algebra", on the other hand, deals with practical computation and real-world applications. It includes solving matrix equations, performing "data analysis", and designing algorithms used in artificial intelligence, 3D modeling, and optimization. Engineers and scientists rely on applied linear algebra to solve real problems from controlling robots to predicting weather patterns.


For advanced learners, there are several "free Linear Algebra books", these books provide both theory and application with exercises for hands-on learning.

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Free Linear Algebra Books
Advanced Linear Algebra: Foundations to Frontiers Geijn
This text teaches "theory", "algorithms", and "computational" techniques in linear algebra. It combines rigorous mathematics with practical programming exercises, videos, and real-world examples, helping students and professionals understand both the concepts and their applications in scientific computing and data analysis.
Algorithms for Sparse Linear Systems by Jennifer Scott
This textbook explains efficient ways to solve large "sparse", "linear", and "computational" systems common in engineering and science. The book covers direct and iterative methods, factorization techniques, and preconditioners, helping readers understand and implement algorithms that take advantage of sparsity for faster, practical solutions.
An Introduction to Determinants by William Thomson -PDF
This text explains "determinants", "matrices", and "linear systems". It teaches how to compute determinants, explore their properties, and apply them to solve linear equations. Students learn how determinants indicate matrix invertibility, aid in Cramer’s Rule, and connect to eigenvalues, volumes, and transformations in linear algebra.
Exercises and Problems in Linear Algebra by John Erdman
This textbook focuses on "practice", "concepts", and "problem-solving". The book offers a wide range of exercises on vector spaces, linear transformations, eigenvalues, and diagonalization, with answers for self-study. It helps students strengthen understanding and build confidence through hands-on, structured practice.
Linear Algebra an Introduction to Abstract Mathemation
This text teaches "abstract", "proof-based", and "computational" aspects of linear algebra. It covers vector spaces, linear maps, eigenvalues, and determinants, helping students build strong reasoning skills while connecting practical calculations to deeper mathematical theory through exercises and clear explanations.
Linear Algebra via Exterior Products by Sergei Winitzki
This textbook teaches "linear algebra", "exterior products", and "vector spaces". It uses a coordinate-free approach to explore determinants, eigenvalues, and the Jordan form, helping students understand the underlying structures of linear algebra. The book blends geometric intuition with algebraic rigor for deeper comprehension.
Linear Algebra with Python by Sean Fitzpatrick - PDF
This text teaches "linear algebra", "Python", and "practical applications". The book combines theory on vector spaces, matrices, eigenvalues, and transformations with interactive coding exercises, allowing students and professionals to learn concepts hands-on while developing programming skills that apply linear algebra to real-world problems efficiently.
Linear Algebra, Theory And Applications Kenneth Kuttler
This text teaches "theory", "applications", and "computational" methods in linear algebra. It covers matrices, vector spaces, linear transformations, determinants, and eigenvalues, blending rigorous explanations with practical examples, helping students understand both the mathematical foundations and how to apply them in real-world problem-solving.
n-Linear Algebra of Type II by W. B. Vasantha Kandasamy
This text teaches "n-linear algebra", "vector spaces", and "eigenvalues". It generalizes traditional linear algebra to handle complex data, introducing n-vector spaces, n-inner products, and n-linear functionals. The book includes problems and applications in coding theory and characteristic polynomials.
Set Linear Algebra and Set Fuzzy Linear Algebra - PDF
This text introduces "set vector spaces", "set linear algebra", and "fuzzy analogues". The book generalizes traditional vector spaces, making them accessible to non-mathematicians. It explores advanced structures like biset bivector spaces, fuzzy n-set vector spaces, and provides over 300 problems for practice.
Special Set Linear Algebra and Special Set Fuzzy Linear
This textbook teaches "set theory", "linear algebra", and "fuzzy systems". It extends traditional vector spaces to finite sets and incorporates fuzziness, helping students and professionals model uncertain or imprecise data in computing, cryptography, and multi-expert systems.
The Theory of Determinants and Their Applications - PDF
This text explains "determinants", "geometry", and "applications". The book explores determinant properties, historical developments, and methods for solving mathematical and geometric problems. It shows how determinants help analyze matrix behavior, understand geometric structures, and apply linear algebra concepts in practical and theoretical contexts.

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