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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.
Author(s): James S. Cook, Liberty University
268 Pages 
Linear Algebra Lecture Notes by Cesar
This note covers systems of linear equations, Row reduction and echelon form, Vector equations, The matrix equation, Homogeneous and nonhomogeneous systems, Linear independence, Introduction to linear mappings, Onto, One to one and standard matrix, Matrix algebra, Invertible matrices, Determinants, Properties of the determinant, Applications of the determinant, Vector spaces, Linear maps, Linear independence, Bases and dimension, The rank theorem, Coordinate systems, Change of basis, Inner products and orthogonality, Eigen values and eigen vectors, The characteristic polynomial, Diagonalization, Diagonalization of symmetric matrices, The PageRank algorithm, Discrete dynamical systems.
Author(s): Cesar O Aguilar, Suny Geneseo
206 Pages
This books covers the following topics: Linear Systems, Vector Spaces, Maps Between Spaces, Determinants, Similarity.
Author(s): Jim Hefferon, Mathematics Department, Saint Michael's College
525 Pages
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
Advanced Linear Algebra by David Surowski
This note explains the following topics: Eigenvalues and Eigenvectors, The spectral theorem, Tensor Products, Fourier Analysis and Quadrtic Reciprocity.
Author(s): David Surowski
157 Pages
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.
Author(s): Leonard Evens
NA Pages
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.
Author(s): Stephen Boyd and Lieven Vandenberghe
473 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