Linear Algebra and Optimization with Applications to Machine Learning Vol.I: Linear Algebra for Computer Vision, Robotics, and Machine Learning

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This book provides the mathematical fundamentals of linear algebra to practicers in computer vision, machine learning, robotics, applied mathematics, and electrical engineering. By only assuming a knowledge of calculus, the authors develop, in a rigorous yet down to earth manner, the mathematical theory behind concepts such as: vectors spaces, bases, linear maps, duality, Hermitian spaces, the spectral theorems, SVD, and the primary decomposition theorem. At all times, pertinent real-world applications are provided. This book includes the mathematical explanations for the tools used which we believe that is adequate for computer scientists, engineers and mathematicians who really want to do serious research and make significant contributions in their respective fields. Sample Chapter(s) Preface Chapter 1: Introduction Request Inspection Copy Contents: Introduction Vector Spaces, Bases, Linear Maps Matrices and Linear Maps Haar Bases, Haar Wavelets, Hadamard Matrices Direct Sums, Rank-Nullity Theorem, Affine Maps Determinants Gaussian Elimination, LU-Factorization, Cholesky Factorization, Reduced Row Echelon Form Vector Norms and Matrix Norms Iterative Methods for Solving Linear Systems The Dual Space and Duality Euclidean Spaces QR-Decomposition for Arbitrary Matrices Hermitian Spaces Eigenvectors and Eigenvalues Unit Quaternions and Rotations in SO(3) Spectral Theorems in Euclidean and Hermitian Spaces Computing Eigenvalues and Eigenvectors Graphs and Graph Laplacians; Basic Facts Spectral Graph Drawing Singular Value Decomposition and Polar Form Applications of SVD and Pseudo-Inverses Annihilating Polynomials and the Primary Decomposition Bibliography Index Readership: Undergraduate and graduate students interested in mathematical fundamentals of linear algebra in computer vision, machine learning, robotics, applied mathematics, and electrical engineering.

Modern Robotics: Mechanics, Planning, and Control (1版)

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【簡介】 Description This introduction to robotics offers a distinct and unified perspective of the mechanics, planning and control of robots. Ideal for self-learning, or for courses, as it assumes only freshman-level physics, ordinary differential equations, linear algebra and a little bit of computing background. Modern Robotics presents the state-of-the-art, screw-theoretic techniques capturing the most salient physical features of a robot in an intuitive geometrical way. With numerous exercises at the end of each chapter, accompanying software written to reinforce the concepts in the book and video lectures aimed at changing the classroom experience, this is the go-to textbook for learning about this fascinating subject. Offers a modern treatment of classical screw theory based on linear algebra and differential equations that is accessible to students with a background in linear algebra, differential equations and first-year physics, and some familiarity with programming Comes with software to accompany the ample algorithmic descriptions for computing covered in the text, allowing students to solve the programming and implementation exercises Includes numerous standard exercises with solutions at the end of each chapter and video lectures for flipped learning courses Can be used either with courses or for self-learning 【目錄】 Table of Contents 1. Preview 2. Configuration space 3. Rigid-body motions 4. Forward kinematics 5. Velocity kinematics and statics 6. Inverse kinematics 7. Kinematics of closed chains 8. Dynamics of open chains 9. Trajectory generation 10. Motion planning 11. Robot control 12. Grasping and manipulation 13. Wheeled mobile robots Appendix A. Summary of useful formulas Appendix B. Other representations of rotations Appendix C. Denavit–Hartenberg parameters Appendix D. Optimization and Lagrange multipliers Bibliography Index.

Introduction to Robotics: Mechanics and Control (4版)

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【簡介】 Description An intuitive introduction to robotic theory and application Since its original publication in 1986, Craig’s Introduction to Robotics: Mechanics and Control has been the leading textbook for teaching robotics at the university level. Blending traditional mechanical engineering material with computer science and control theoretical concepts, the text covers a range of topics, including rigid-body transformations, forward and inverse positional kinematics, velocities and Jacobians of linkages, dynamics, linear and non-linear control, force control methodologies, mechanical design aspects, and robotic programming. The 4th Edition features a balance of application and theory, introducing the science and engineering of mechanical manipulation--establishing and building on foundational understanding of mechanics, control theory, and computer science. With an emphasis on computational aspects of problems, the text aims to present material in a simple, intuitive way. 【目錄】 Table of Contents 1. Introduction 2. Spatial Transformations 3. Forward Kinematics 4. Inverse Kinematics 5. Velocities, Static Forces, and Jacobians 6. Dynamics 7. Trajectory Planning 8. Mechanical Design of Robots 9. Linear Control 10. Non-Linear Control 11. Force Control 12. Programming Languages and Systems 13. Simulation and Off-Line Programming