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Linear Algebra Books

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.

A Brief Introduction to Linear Algebra

This note covers the following topics: Linear Algebra, Matrix Algebra, Homogeneous Systems and Vector Subspaces, Basic Notions, Determinants and Eigenvalues, Diagonalization, The Exponential of a Matrix, Applications,Real Symmetric Matrices, Classification of Conics and Quadrics, Conics and the Method of Lagrange Multipliers, Normal Modes.

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s NAPages

Introduction to Applied Linear Algebra

This book is meant to provide an introduction to vectors, matrices, and least squares methods, basic topics in applied linear algebra. Our goal is to give the beginning student, with little or no prior exposure to linear algebra, a good grounding in the basic ideas, as well as an appreciation for how they are used in many applications, including data fitting, machine learning and artificial intelligence, tomography, image processing, finance, and automatic control systems. Topics covered includes: Vectors, Norm and distance, Clustering, Matrices, Linear equations, Matrix multiplication, Linear dynamical systems, Least squares, Multi-objective least squares, Constrained least squares.

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s 473Pages

Linear Algebra Notes by David A. Santos

The purpose with these notes is to introduce students to the concept of proof in linear algebra in a gentle manner. Topics covered includes: Matrices and Matrix Operations, Linear Equations, Vector Spaces, Linear Transformations, Determinants, Eigenvalues and Eigenvectors, Linear Algebra and Geometry.

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s 270Pages

Linear Algebra, Theory And Applications

This is a book on linear algebra and matrix theory. It provides an introduction to various numerical methods used in linear algebra. This is done because of the interesting nature of these methods. Topics covered includes: Matrices And Linear Transformations, Determinant, Row Operations, Factorizations, Vector Spaces And Fields, Linear Transformations, Inner Product Spaces, Norms For Finite Dimensional Vector Spaces.

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s 503Pages

Linear Algebra A free Linear Algebra Textbook and Online Resource

This textbook is suitable for a sophomore level linear algebra course taught in about twenty-five lectures. It is designed both for engineering and science majors, but has enough abstraction to be useful for potential math majors. Our goal in writing it was to produce students who can perform computations with linear systems and also understand the concepts behind these computations.

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s 436Pages

Fundamentals of Linear Algebra and Optimization

This note covers the following topics: Vector Spaces, Bases, Linear Maps, Matrices and Linear Maps, Direct Sums, Affine Maps, The Dual Space, Duality, Gaussian Elimination, LU, Cholesky, Echelon Form, Determinants, Vector Norms and Matrix Norms, Eigenvectors and Eigenvalues, Iterative Methods for Solving Linear Systems, Euclidean Spaces, Hermitian Spaces, Spectral Theorems, The Finite Elements Method, Singular Value Decomposition and Polar Form, Applications of SVD and Pseudo-Inverses, Annihilating Polynomials, Differential Calculus, Schur Complements and Applications, Linear Programming and Duality, Hilbert Spaces, Soft Margin Support Vector Machines.

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s 925Pages

Introductory Notes in Linear Algebra for the Engineers

This book is addressed primarely to second and third year college engineering students who have already had a course in calculus and analytic geometry. It is the result of lecture notes given by the author at Arkansas Tech University. Topics covered includes: Linear Systems of Equations, Matrices, Determinants, The Theory of Vector Spaces, Eigenvalues and Eigenvectors, Linear Transformation.

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s 221Pages

Linear Algebra I by Ronald van Luijk

This note explains the following topics: Vector spaces, The field of complex numbers, Linear maps, Subspaces, Matrices, Linear independence and dimension, Ranks, Linear maps and matrices, Determinants, Eigenvalues and Eigenvectors.

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s 156Pages

Fundamentals of Linear Algebra

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.

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s 412Pages

Course Material for Linear Algebra I

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.

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s NAPages

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

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.

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s 56Pages

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

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.

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s 95Pages

Linear Algebra II Lecture Notes (PDF 61P)

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.

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s 61Pages

Linear Algebra in Twenty Five Lectures (PDF 395P)

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.

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s 395Pages

Lecture Notes for Linear Algebra (PDF 268P)

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.

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s 268Pages

Lecture Notes on Linear Algebra (PDF 220P)

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

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s 220Pages

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

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.

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s 212Pages

A Course In Algebraic Number Theory

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

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s NAPages

Algebraic Number Theory .pdf

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- Fermat’s Last Theorem, Absolute Values- Local Fieldsand Global Fields.

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s 164Pages

College Algebra

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s 356Pages

Course of Linear Algebra and Multidimensional Geometry

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A Course In Commutative Algebra

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.

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s NAPages

A Pari/GP Tutorial

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.

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s 20Pages

An Introduction to Linear Algebra

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

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s 27Pages

Fundamentals of Linear Algebra

This book is not a ”traditional” book in the sense that it does not include any applications to the material discussed. Its aim is solely to learn the basic theory of linear algebra within a semester period. Topics covered includes: Linear Systems, Matrices, Determinants, The Theory of Vector Spaces, Eigenvalues and Diagonalization and Linear Transformations.

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s 196Pages

A Course in Universal Algebra

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s NAPages

Algebra and Number Theory A. Baker

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Review of Algebra

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Algebra Cheat Sheet

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Workbook in Higher Algebra

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A Geometric Review of Linear Algebra

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ELEMENTARY LINEAR ALGEBRA

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An Algebra Refresher

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Linear Algebra Hefferon J (Mirror)

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Linear Algebra2

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Linear Algebra, Infinite Dimensions, and Maple

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A Computational Introduction to Number Theory and Algebra (Version 1)

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A First Course in Linear Algebra

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Elements of Abstract and Linear Algebra

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Notes on Linear Algebra

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Algebra

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Algebra Review in Ten Lessons

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Group Characters, Symmetric Functions, and the Hecke Algebra

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PROBLEMS IN ALGEBRAIC COMBINATORICS

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Algebraic Curves

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Introduction to Algebraic Varieties

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Advanced Linear Algebra lecture notes (with real algorithm for the real Jordan form)

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Basic Linear Algebra (PDF 73p)

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Toeplitz and Circulant Matrices

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Lectures on Matrices

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An Invitation to General Algebra and Universal Constructions

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