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 Notes by David A. SantosDavid A. SantosPDF
| 270 Pages
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.
Linear Algebra, Theory And ApplicationsKenneth KuttlerPDF
| 503 Pages
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.
Linear Algebra A free Linear Algebra Textbook and Online ResourceDavid Cherney,
Tom Denton, Rohit Thomas and Andrew WaldronPDF
| 436 Pages
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.
Fundamentals of Linear Algebra and OptimizationJean Gallier and Jocelyn
| 925 Pages
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.
Exercises and Problems in Linear AlgebraJohn M. ErdmanPDF
| 196 Pages
This collection of
exercises is designed to provide a framework for discussion in a junior level
linear algebra class conducted fairly regularly at Portland State University.
Topics covered includes: Matrices And Linear Equations, Vector Spaces , Linear
Maps Between Vector Spaces , Spectral Theory Of Vector Spaces, The Geometry Of
Inner Product Spaces , Adjoint Operators, Spectral Theory Of Inner Product
Introductory Notes in Linear Algebra for the EngineersMarcel B. FinanPDF
| 221 Pages
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.
Linear Algebra I by Ronald van LuijkRonald van LuijkPDF
| 156 Pages
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.
Fundamentals of Linear AlgebraJames B. CarrellPDF
| 412 Pages
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 IUniversity of OxfordOnline
| NA Pages
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.
Algebraic Curves NotesNigel Hitchin and Balazs SzendroiPDF
| 67 Pages
This lecture note
explains the concepts of projective space and curves in the projective plane.
Covered topics are: Projective spaces, Plane curves, Intersections of curves,
The genus of a curves and Riemann-Roch theorem.
Linear Algebraic Groups and K TheoryUniversity of BielefeldPDF
| 46 Pages
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
Linear Algebra lecture notes Martin Bright and Daan Krammer (PDF 56P)Martin
Bright and Daan KrammerPDF
| 56 Pages
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)Simon J.A. MalhamPDF
| 95 Pages
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)John C. Bowman, University of
| 61 Pages
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)Tom Denton and Andrew WaldronPDF
| 395 Pages
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)James S. Cook, Liberty UniversityPDF
| 268 Pages
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)Eleftherios GkioulekasPDF
| 220 Pages
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)D.
Hobby and R. McKenziePDF
| 212 Pages
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 TheoryRobert
B. Ash, Professor Emeritus, MathematicsOnline
| NA Pages
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 .pdfJ.S.
| 164 Pages
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
|Course of Linear Algebra and Multidimensional Geometry|
A Course In Commutative AlgebraRobert
B. Ash, Professor Emeritus, MathematicsOnline
| NA Pages
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 TutorialRobert
| 20 Pages
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 AlgebraBarry
M. Wise and Neal B. GallagherPDF
| 27 Pages
This article reviews the basics of linear algebra
and provides the reader with the foundation required for
understanding most chemometrics literature.
Fundamentals of Linear AlgebraMarcel
| 196 Pages
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
|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 Lecture notes|
|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|
|Algebra Review in Ten Lessons|
|Group Characters, Symmetric Functions, and the Hecke Algebra|
|Elementary algebra book|
|PROBLEMS IN ALGEBRAIC COMBINATORICS|
|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|