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
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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.
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2969
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2821
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Elementary Linear Algebra 8/E 修訂版 (8版)
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【簡介】
【目錄】
1 Systems of Linear Equations
2 Matrices
3 Determinants
4 Vector Spaces
5 Inner Product Spaces
6 Linear Transformations
7 Eigenvalues and Eigenvectors
8 Complex Vector Spaces (online)*
9 Linear Programming (online)*
10 Numerical Methods (online)*
Appendix
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1300
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Advanced Linear Algebra: With an Introduction to Module Theory (1版)
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【簡介】
Certain essential concepts in linear algebra cannot be fully explained in a first course. This is due to a lack of algebraic background for most beginning students. On the other hand, these concepts are taken for granted in most of the mathematical courses at graduate school level. This book will provide a gentle guidance for motivated students to fill the gap. It is not easy to find other books fulfilling this purpose. This book is a suitable textbook for a higher undergraduate course, as well as for a graduate student's self-study. The introduction of set theory and modules would be of particular interest to students who aspire to becoming algebraists.
There are three parts to this book. One is to complete the discussion of bases and dimension in linear algebra. In a first course, only the finite dimensional vector spaces are treated, and in most textbooks, it will assume the scalar field is the real number field. In this book, the general case of arbitrary dimension and arbitrary scalar fields is examined. To do so, an introduction to cardinality and Zorn's lemma in set theory is presented in detail. The second part is to complete the proof of canonical forms for linear endomorphisms and matrices. For this, a generalization of vector spaces, and the most fundamental results regarding modules are introduced to readers. This will provide the natural entrance into a full understanding of matrices. Finally, tensor products of vector spaces and modules are briefly discussed.
【目錄】
1.Modules and Vector Spaces
2.Linear Maps
3.Determinant
4.Canonical Forms
5.A Brief Introduction to the Tensor Product
原價:
1260
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1172
現省:
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