Technical Books

This book is a course in mathematical analysis written in Russian. This book contains below topics, Foundations of mathematics, Functions of one real variable, Functions of several real variables.

This book contains below topics, The Real Numbers, Limits of Functions and Continuity, Differentiating Functions of a Single Variable, Integrating Functions of a Single Variable, Infinite Series of Numbers and Infinite Products, Sequences and Series of Functions.

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.

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.

This note explains the following topics, Eigenvalues and Eigenvectors, The spectral theorem, Tensor Products, Fourier Analysis and Quadrtic Reciprocity.

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.

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.

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.

This book contains below topics, Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic Equation of Matrix, Matrix Dot Product.

This book contains below topics, Systems of Linear Equations, Row Reduction, Vector Geometry, Linear Transformations, Eigenvalues, Orthogonality, Determinants.

This book contains below topics, Systems of Linear Equations, Vectors, Matrices, Linear Transformations, Vector Spaces, Determinants, Eigenvalues and Eigenvectors, Orthogonality.

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.

This note covers the following topics, Matrix and Lie Groups, Dynamics and Control on Matrix Groups, Optimality and Riccati Equations, Geometric Control.

This is an open source book written by Francisco Bulnes. The purpose of this book is to present a complete course on global analysis topics and establish some orbital applications of the integration on topological groups and their algebras to harmonic analysis and induced representations in representation theory.

This note covers the following topics, Universal envelopping algebras, Levis theorem, Serres theorem, KacMoody Lie algebra, The Kostants form of the envelopping algebra and A beginning of a proof of the Chevalleys theorem.