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Free Linear Algebra Books

Abstract Algebra
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Linear Algebra
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Commutative Algebra
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Complex Algebra
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Elliptic Curves
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Geometric Algebra
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Groups Theory
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Higher Algebra
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Homological Algebra
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Lie Algebra
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Differential Algebra
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Rings and Fileds
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Geometry
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Algebraic Geometry
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Differential Geometry
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Fractals
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Riemannian Geometry
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Mathematical Analysis
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Complex Analysis
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Functional Analysis
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Differential Analysis
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Fourier Analysis
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Harmonic Analysis
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Numerical Analysis
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Real Analysis
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Topology
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Algebraic Topology
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Differential Topology
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Geometric Topology
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K-theory
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Applied Mathematics
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Calculus
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Differential Equations
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Combinatorics
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Discrete Mathematics
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Graph Theory
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Number Theory
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Probability Theory
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Set Theory
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Trigonometry
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Category Theory
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Constants & Numerical Sequences
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Basic Mathematics
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Classical Analysis
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History of Mathematics
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Arithmetic Geometry
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Mathematical Series
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Modern Geometry
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Basic Algebra
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Differential Equations
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This section contains free e-books and guides on Linear Algebra, some of the resources in this section can be viewed online and some of them can be downloaded.

Linear Algebra Books
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Fundamentals of Linear Algebra

PDF | 412 Pages | English
This textbook is meant to be a mathematically complete and rigorous introduction to abstract linear algebra for undergraduates, possibly even first year students, specializing in mathematics. Author tried very hard to emphasize the fascinating and important interplay between algebra and geometry.

 
Course Material for Linear Algebra I

Online | NA Pages | English
Linear algebra pervades and is fundamental to algebra, geometry, analysis, applied mathematics, statistics, and indeed most of mathematics. This course note lays the foundations, concentrating mainly on vector spaces and matrices over the real and complex numbers.

 
Linear Algebraic Groups and K Theory

PDF | 46 Pages | English
These lectures notes are organized as 6 sections. Sections are: The group structure of SLn over a field, Linear algebraic groups over field, Root systems, Chevalley groups, K-theoretic results related to Chevalley group, structure and classification of almost simple algebraic groups, Further K-theoretic results for simple algebraic groups.

 
Linear Algebra lecture notes Martin Bright and Daan Krammer (PDF 56P)

PDF | 56 Pages | English
This book explains the following topics related to Linear Algebra: Number systems and fields, Vector spaces, Linear independence, spanning and bases of vector spaces, Subspaces, Linear transformations, Matrices, Linear transformations and matrices, Elementary operations and the rank of a matrix, The inverse of a linear transformation and of a matrix, Change of basis and equivalent matrices.

 
Differential Equations and Linear Algebra Lecture Notes (PDF 95P)

PDF | 95 Pages | English
This book explains the following topics related to Differential Equations and Linear Algebra: Linear second order ODEs, Homogeneous linear ODEs, Non-homogeneous linear ODEs, Laplace transforms, Linear algebraic equations, Linear algebraic eigenvalue problems and Systems of differential equations.

 
Linear Algebra II Lecture Notes (PDF 61P)

PDF | 61 Pages | English
This book explains the following topics related to Linear Algebra: Vectors, Linear Equations, Matrix Algebra, Determinants, Eigenvalues and Eigenvectors, Linear Transformations, Dimension, Similarity and Diagonalizability, Complex Numbers, Projection Theorem, Gram-Schmidt Orthonormalization, QR Factorization, Least Squares Approximation, Orthogonal (Unitary) Diagonalizability, Systems of Differential Equations, Quadratic Forms, Vector Spaces and the Pseudoinverse.

 
Linear Algebra in Twenty Five Lectures (PDF 395P)

PDF | 395 Pages | English
This note emphasize the concepts of vector spaces and linear transformations as mathematical structures that can be used to model the world around us. Topics covered includes: Gaussian Elimination, Elementary Row Operations, Vector Spaces, Linear Transformations, Matrices, Elementary Matrices and Determinants, Eigenvalues and Eigenvectors, Diagonalization, Kernel, Range, Nullity, Rank, Gram-Schmidt and Orthogonal Complements.

 
Lecture Notes for Linear Algebra (PDF 268P)

PDF | 268 Pages | English
These notes are intended for someone who has already grappled with the problem of constructing proofs.This book covers the following topics:  Gauss-Jordan elimination, matrix arithmetic, determinants , linear algebra, linear transformations, linear geometry, eigenvalues and eigenvectors.

 
Lecture Notes on Linear Algebra (PDF 220P)

PDF | 220 Pages | English
This book covers the following topics: Brief introduction to Logic and Sets, Brief introduction to Proofs, Basic Linear Algebra, Eigenvalues and Eigenvectors, Vector Spaces.

 
The Structure of Finite Algebras (D. Hobby and R. McKenzie)

PDF | 212 Pages | English
This book covers the following topics: Basic concepts and notation, Tight lattices, Tame quotients, Abelian and solvable algebras, The structure of minimal algebras, The types of tame quotients, Labeled congruence lattices, Solvability and semi-distributivity, Congruence modular varieties, Malcev classification and omitting types, Residually small varieties, Decidable varieties, Free spectra, Tame algebras and E-minimal algebras, Simple algebras in varieties.

 
A Course In Algebraic Number Theory

Online | NA Pages | English
This is a text for a basic course in algebraic number theory. This book covers the following topics: Norms, Traces and Discriminants, Dedekind Domains, Factoring of Prime Ideals in Extensions, The Ideal Class Group, The Dirichlet Unit Theorem, Cyclotomic Extensions, Factoring of Prime Ideals in Galois Extensions and Local Fields

 
Algebraic Number Theory .pdf

PDF | 164 Pages | English
These notes are concerned with algebraic number theory, and the sequel with class field theory. Topics covered includes: Preliminaries from Commutative Algebra, Rings of Integers, Dedekind Domains- Factorization, The Unit Theorem, Cyclotomic Extensions- Fermatís Last Theorem, Absolute Values- Local Fieldsand Global Fields.

 
College Algebra

PDF | 356 Pages | English


 
Course of Linear Algebra and Multidimensional Geometry
A Course In Commutative Algebra

Online | NA Pages | English
This book covers the following topics: Ring Theory Background, Primary Decomposition and Associated Primes, Integral Extensions, Valuation Rings, Completion, Dimension Theory, Depth, Homological Methods and Regular Local Rings.

 
A Pari/GP Tutorial

PDF | 20 Pages | English
This book covers the following topics: Pari Types, Transcendental and Other Nonrational Functions, Arithmetic Functions, Polynomials and Power Series, Sums, Products and Integrals, Basic Programming, Algebraic Number Theory and Elliptic Curves.

 
An Introduction to Linear Algebra

PDF | 27 Pages | English
This article reviews the basics of linear algebra and provides the reader with the foundation required for understanding most chemometrics literature.

 
An Introduction To Linear Algebra Kenneth Kuttler
Linear Algebra test questions
A Course in Universal Algebra
Algebra and Number Theory A. Baker
Review of Algebra
Algebra Cheat Sheet
Workbook in Higher Algebra
A Geometric Review of Linear Algebra
ELEMENTARY LINEAR ALGEBRA
An Algebra Refresher
Linear Algebra Hefferon J (Mirror)
Linear Algebra wchen
Linear Algebra2
Linear Algebra, Infinite Dimensions, and Maple
A Computational Introduction to Number Theory and Algebra (Version 1)
A First Course in Linear Algebra
Elements of Abstract and Linear Algebra
Notes on Linear Algebra
Geometric Algebra Primer
Miscellaneous Topics in First Year Mathematics
Algebra
Algebra Review in Ten Lessons
Group Characters, Symmetric Functions, and the Hecke Algebra
Algebraic Fractions
PROBLEMS IN ALGEBRAIC COMBINATORICS
Algebraic Curves
Algebraic Logic
Introduction to Algebraic Varieties
Advanced Linear Algebra lecture notes (with real algorithm for the real Jordan form)
Basic Linear Algebra (PDF 73p)
Toeplitz and Circulant Matrices
Lectures on Matrices
An Invitation to General Algebra and Universal Constructions
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