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A First Course in Linear Algebra by Ilijas Farah and K. Kuttler
The contents of this book include: Systems of Equations, Matrices, Determinants, Linear Transformations, Complex Numbers, Spectral Theory, Some Curvilinear Coordinate Systems, Vector Spaces.
Author(s): Ilijas Farah, K. Kuttler
608 Pages
Lecture notes on Advanced Linear Algebra
This note covers the following topics: Motivation, linear spaces, and isomorphisms, Subspaces, linear dependence and independence, Bases, Dimension, direct sums, and isomorphism, Quotient spaces and dual spaces, Linear maps, nullspace and range, Nullity and rank, Matrices, Changing bases, Conjugacy, types of operators, dual space, determinants.
Author(s): Vaughn Climenhaga
145 Pages
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.
Author(s): David Cherney, Tom Denton, Rohit Thomas and Andrew Waldron
436 Pages
Exercises and Problems in Linear Algebra
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 Spaces.
Author(s): John M. Erdman
196 Pages
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.
Author(s): Ronald van Luijk
156 Pages
Lecture notes on linear algebra by David Lerner
These are lecture notes for a first course in linear algebra; the prerequisite is a good course in calculus. The notes are quite informal, but they have been carefully read and criticized by two sections of honors students, and their comments and suggestions have been incorporated. Topics covered includes: Matrices and matrix algebra, Elementary row operations and their corresponding matrices, Homogeneous systems, Square matrices, inverses and related matters, The derivative as a matrix, Subspaces, Linearly dependent and independent sets, Basis and dimension of subspaces, 3 The rank-nullity (dimension) theorem, Eigenvalues and eigenvectors, Orthogonal projections and orthogonal matrices, Symmetric and skew-symmetric matrices.
Author(s): David Lerner, University of Kansas
120 Pages
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.
Author(s): James B. Carrell
412 Pages
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.
Author(s): Tom Denton and Andrew Waldron
395 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 Global Fields.
Author(s): J.S. Milne
164 Pages
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A First Course in Linear Algebra
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Basic Linear Algebra (PDF 73p)
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An Invitation to General Algebra and Universal Constructions
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