给出几何代数在理论物理中的应用

The goal of the Volume I Geometric Algebra for Computer Vision, Graphics and Neural Computing is to present a unified mathematical treatment of diverse problems in the general domain of artificial intelligence and associated fields using Clifford, or geometric, algebra. Geometric algebra provides a rich and general mathematical framework for Geometric Cybernetics in order to develop solutions, concepts and computer algorithms without losing geometric insight of the problem in question. Current mathematical subjects can be treated in an unified manner without abandoning the mathematical system of geometric algebra for instance: multilinear algebra, projective and affine geometry, calculus on manifolds, Riemann geometry, the representation of Lie algebras and Lie groups using bivector algebras and conformal geometry. By treating a wide spectrum of problems in a common language, this Volume I offers both new insights and new solutions that should be useful to scientists, and engineers working in different areas related with the development and building of intelligent machines. Each chapter is written in accessible terms accompanied by numerous examples, figures and a complementary appendix on Clifford algebras, all to clarify the theory and the crucial aspects of the application of geometric algebra to problems in graphics engineering, image processing, pattern recognition, computer vision, machine learning, neural computing and cognitive systems.

Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.

Basics of Linear Algebra for Machine Learning.zip 机器学习的线性代数基础 课程代码

随机矩阵 随机矩阵理论的软件包。 希望增加足够的功能并在2021年8月发布。 例子 随机矩阵理论 随机矩阵模型 生成3 x 3随机Unit矩阵运行 RandomUnitaryMatrix(3)或等效 rand(Haar(2,3)) 生成3 x 3随机正交矩阵 RandomOrthogonalMatrix(3)或等效 rand(Haar(1,3)) 随机线性代数 如果A是一个乘m矩阵，而B是一个乘w矩阵。 运行RandomSamplingMatrix(A,B,k=2)将生成大小为m×k的随机采样矩阵S。 其中E（SS'）= I，而E（ASS'B）= AB。 对于定义，请检查代码或在2.2节末尾（在2.3节之前）查找S：= SD。

线性代数学习经典图书，国外经典图书，英文文字版

线性代数应该这样学Liner Algebra Done Right(中文) 线性代数应该这样学Liner Algebra Done Right(中文)

GTM Hungerford Algebra 英文 可搜索版本

代数圣经级教材，包含了群，环等现代抽象代数的结构与浅析。证明和编排不是特别科学，阅读需要一定基础。

APPLIED NUMERICAL LINEAR ALGEBRA James W. Demmel University of California Berkeley, California Society for Industrial and Applied Mathematics Philadelphia Contents Preface ix 1 Introduction 1 1.1 Basic Notation 1 1.2 Standard Problems of Numerical Linear Algebra 1 1.3 General Techniques 2 1.3.1 Matrix Factorizations 3 1.3.2 Perturbation Theory and Condition Numbers 4 1.3.3 Effects of Roundoff Error on Algorithms 5 1.3.4 Analyzing the Speed of Algorithms 5 1.3.5 Engineering Numerical Software 6 1.4 Example: Polynomial Evaluation 7 1.5 Floating Point Arithmetic 9 1.5.1 Further Details 12 1.6 Polynomial Evaluation Revisited 15 1.7 Vector and Matrix Norms 19 1.8 References and Other Topics for Chapter 1 23 1.9 Questions for Chapter 1 24 2 Linear Equation Solving 31 2.1 Introduction 31 2.2 Perturbation Theory 32 2.2.1 Relative Perturbation Theory 35 2.3 Gaussian Elimination 38 2.4 Error Analysis 44 2.4.1 The Need for Pivoting 45 2.4.2 Formal Error Analysis of Gaussian Elimination 46 2.4.3 Estimating Condition Numbers 50 2.4.4 Practical Error Bounds 54 2.5 Improving the Accuracy of a Solution 60 2.5.1 Single Precision Iterative Refinement 62 2.5.2 Equilibration 62 2.6 Blocking Algorithms for Higher Performance 63 2.6.1 Basic Linear Algebra Subroutines (BLAS) 66 2.6.2 How to Optimize Matrix Multiplication 67 2.6.3 Reorganizing Gaussian Elimination to Use Level 3 BLAS 72 2.6.4 More About Parallelism and Other Performance Issues . 75 vi Contents 2.7 2.8 2.9 Special Linear Systems 2.7.1 Real Symmetric Positive Definite Matrices 2.7.2 Symmetric Indefinite Matrices 2.7.3 Band Matrices 2.7.4 General Sparse Matrices 2.7.5 Dense Matrices Depending on Fewer Than O(n2) Pa- rameters References and Other Topics for Chapter 2 Questions for Chapter 2 76 76 79 79 83 90 93 93 3 Linear Least Squares Problems 101 3.1 Introduction 101 3.2 Matrix Factorizations That Solve the Linear Least Squares Prob- lem 105 3.2.1 Normal Equations 106 3.2.2 QR Decomposition 107 3.2.3 Singular Value Decompos