CONTENTS ContentsofBasic Algebra x Preface xi List of Figures xv Dependence amongChapters xvi Guide forthe Reader xvii Notation and Terminology xxi I. TRANSITIONTO MODERNNUMBERTHEORY 1 1. Historical Background 1 2. Quadratic Reciprocity 8 3. Equival
Contents Preface to the Third Edition, vii Preface to the Second Edition, ix Preface to the First Edition, xi Preliminaries, 1 Part 1: Preliminaries, 1 Part 2: Algebraic Structures, 17 Part I---Basic Linear Algebra, 33 1 Vector Spaces, 35 Vector Spa
Abstract—This paper introduces a multilinear principal com- ponent analysis (MPCA) framework for tensor object feature extraction. Objects of interest in many computer vision and pattern recognition applications, such as 2-D/3-D images and video seq
We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higher-order tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, fir
This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or N-way array. Decompositions of higher-order tensors (i.e., N-way arrays with N ≥ 3) have applicatio
关于张量在HSI中的应用 一种TD分解 widespread use of multisensor technology and the emergence of big data sets have highlighted the limitations of standard flat-view matrix models and the necessity to move toward more versatile data analysis tools. We show that hi
Geometric Algebra Applications Vol. I: Computer Vision, Graphics and Neurocomputing pdf 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
Modern applications in engineering and data science are increasingly based on multidimensional data of exceedingly high volume, variety, and structural richness. However, standard machine learning algo- rithms typically scale exponentially with data
在抽象代数中,交换代数旨在探讨交换环及其理想,以及交换环上的模Contents
Introduction
for the bes
r
2
requisites
6
a First Cot
ourse
howled e
0 Elementary Definitions
11
0. 1 Ringy and Ides
0.2 Unique Factorization
0 3 Modules
Basic constructions
19
1 Roots of c
tative Algebra
21
1.
Multilinear/tensor extensions of manifold learning based algorithms have been widely used in computer vision and pattern recognition. This paper first provides a systematic analysis of the multilinear extensions for the most popular methods by using
