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Fundamentals of Linear Algebra and Optimization
This 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 Pseudo-Inverses, Annihilating Polynomials, Differential Calculus, Schur Complements and Applications, Linear Programming and Duality, Hilbert Spaces, Soft Margin Support Vector Machines.
Author(s): Jean Gallier and Jocelyn Quaintance
925 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, Multiobjective least squares, Constrained least squares.
Author(s): Stephen Boyd and Lieven Vandenberghe
473 Pages
This book contains below topics, Vector Spaces, Finite Dimensional Vector Spaces, Linear Maps, Polynomials, Eigenvalues and Eigenvectors, Inner Product Spaces, Operators on Inner Product Spaces, Operators on Complex Vector Spaces, Operators on Real Vector Spaces, Trace and Determinant.
Author(s): Sheldon Axler
404 Pages
This book contains below topics, Systems of Linear Equations, Vectors, Matrices, Linear Transformations, Vector Spaces, Determinants, Eigenvalues and Eigenvectors, Orthogonality.
Author(s): David Cherney, Tom Denton, Rohit Thomas, Andrew Waldron
395 Pages
A First Course in Linear Algebra Study Guide for the Undergraduate Linear Algebra Course
This book contains below topics, Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic Equation of Matrix, Matrix Dot Product.
Author(s): Mohammed K A Kaabar
132 Pages
Course of linear algebra and multidimensional geometry
This book contains below topics, Linear vector spaces and linear mappings, The sets and mappings, Linear vector spaces, Linear dependence and linear independence, Spanning systems and bases, Intersections and sums of subspaces, Cosets of a subspace The concept of factorspace, Linear mappings, The matrix of a linear mapping, Linear operators, Projection operators.
Author(s): Ruslan Sharipov
143 Pages
Lectures on Linear Algebra over Division Ring
This note contains below topics, Lectures on Linear Algebra over Division Ring, Biring of Matrices, Representation of Universal Algebra, Representation of Group, Vector Space over Division Ring, Basis Manifold, Linear Map of RcdVector Space, Product of Representations, Geometry of Division Ring.
Author(s): Aleks Kleyn
321 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
Linear Algebra A free Linear Algebra Textbook and Online Resource
This 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.
Author(s): David Cherney, Tom Denton, Rohit Thomas and Andrew Waldron
436 Pages