Basic Linear Algebra (PDF 73p)

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

Linear Algebra Jim Hefferon

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

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, Theory And Applications

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.

Author(s): Kenneth Kuttler

503 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