Advanced Linear Algebra lecture notes (with real algorithm for the real Jordan form)

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

Linear Algebra Done Right

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

Linear Algebra

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

Lecture Notes on Randomized Linear Algebra

This note contains below topics, Approximating Matrix Multiplication, Scalar and Matrix Concentration, Concentration and Matrix Multiplication, Matrix Multiplication and Random Projections, Sampling and Projections for Least squares Approximation, Fast Random Projections and FJLT, Randomized Least squares Approximation in Practice, Additive error Low rank Matrix Approximation, Relative error Low rank Matrix Approximation, Randomized Low rank Approximation in Practice, Low rank Matrix Approximation with Element wise Sampling, Element wise Sampling and Matrix Completion, Element wise Sampling of Graphs and Linear Equation Solving.

Author(s): Michael W. Mahoney

188 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

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

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