

This section contains free ebooks 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 AlgebraLeonard
EvensOnline  NA Pages  EnglishThis 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.
 Introduction to Applied Linear AlgebraStephen Boyd and Lieven VandenberghePDF  473 Pages  EnglishThis 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, Multiobjective least squares, Constrained least squares.
 Linear Algebra Notes by David A. SantosDavid A. SantosPDF  270 Pages  EnglishThe 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  EnglishThis 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  EnglishThis textbook is suitable for a
sophomore level linear algebra course taught in about twentyfive 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
QuaintancePDF  925 Pages  EnglishThis 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 PseudoInverses, 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  EnglishThis 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
Spaces.
 Introductory Notes in Linear Algebra for the EngineersMarcel B. FinanPDF  221 Pages  EnglishThis 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  EnglishThis 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  EnglishThis 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  EnglishLinear 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 TheoryUniversity of BielefeldPDF  46 Pages  EnglishThese 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,
Ktheoretic results related to Chevalley group, structure and classification of
almost simple algebraic groups, Further Ktheoretic results for simple algebraic
groups.
 Linear Algebra lecture notes Martin Bright and Daan Krammer (PDF 56P)Martin
Bright and Daan KrammerPDF  56 Pages  EnglishThis 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  EnglishThis
book explains the following topics related to Differential Equations and Linear
Algebra: Linear second order ODEs, Homogeneous linear ODEs, Nonhomogeneous
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
AlbertaPDF  61 Pages  EnglishThis 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, GramSchmidt
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  EnglishThis
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,
GramSchmidt and Orthogonal Complements.
 Lecture Notes for Linear Algebra (PDF 268P)James S. Cook, Liberty UniversityPDF  268 Pages  EnglishThese notes are
intended for someone who has already grappled with the problem of constructing
proofs.This book covers the following topics: GaussJordan elimination,
matrix arithmetic, determinants , linear algebra, linear transformations, linear
geometry, eigenvalues and eigenvectors.
 Lecture Notes on Linear Algebra (PDF 220P)Eleftherios GkioulekasPDF  220 Pages  EnglishThis
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  EnglishThis 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 semidistributivity,
Congruence modular varieties, Malcev classification and omitting types,
Residually small varieties, Decidable varieties, Free spectra, Tame algebras and
Eminimal algebras, Simple algebras in varieties.
 A Course In Algebraic Number TheoryRobert
B. Ash, Professor Emeritus, MathematicsOnline  NA Pages  EnglishThis
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.
MilnePDF  164 Pages  EnglishThese 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.
  Course of Linear Algebra and Multidimensional Geometry  A Course In Commutative AlgebraRobert
B. Ash, Professor Emeritus, MathematicsOnline  NA Pages  EnglishThis
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
B. AshPDF  20 Pages  EnglishThis 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  EnglishThis article reviews the basics of linear algebra
and provides the reader with the foundation required for
understanding most chemometrics literature.
 Fundamentals of Linear AlgebraMarcel
B. FinanPDF  196 Pages  EnglishThis 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.
 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 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  Algebra  Algebra Review in Ten Lessons  Group Characters, Symmetric Functions, and the Hecke Algebra  PROBLEMS IN ALGEBRAIC COMBINATORICS  Algebraic Curves  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 








