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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 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
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
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
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Linear Algebra Hefferon J (Mirror)
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A Computational Introduction to Number Theory and Algebra (Version 1)
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Advanced Linear Algebra lecture notes (with real algorithm for the real Jordan form)
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Toeplitz and Circulant Matrices
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