文件名称：Morgan.Kaufmann.Geometric.Tools.For.Computer.Graphics
文件大小：12.15MB
文件格式：PDF
更新时间：2012-08-05 08:12:05
Morgan.Kaufmann.Geometric.Tools.For.Computer.Graphics
1 Introduction ..................................................................... 1 How to Use This Book ............................................................ 1 Issues of Numerical Computation ........................................... 2 Low-Level Issues ................................................................................. 2 High-Level Issues ................................................................................ 4 A Summary of the Chapters ................................................... 6 2 Matrices and Linear Systems ......................................... 9 Introduction ............................................................................. 9 Motivation ............................................................................................ 9 Organization ........................................................................................ 13 Notational Conventions ....................................................................... 14 Tuples ..................................................................................... 14 Definition .............................................................................................. 15 Arithmetic Operations .......................................................................... 16 Matrices .................................................................................. 16 Notation and Terminology ................................................................... 17 Transposition ....................................................................................... 17 Arithmetic Operations .......................................................................... 18 Matrix Multiplication ............................................................................. 20 Linear Systems ....................................................................... 24 Linear Equations .................................................................................. 24 Linear Systems in Two Unknowns ...................................................... 26 General Linear Systems ...................................................................... 29 Row Reductions, Echelon Form, and Rank ......................................... 30 Square Matrices ...................................................................... 32 Diagonal Matrices ................................................................................ 32 Triangular Matrices .............................................................................. 34 The Determinant .................................................................................. 34 Inverse ................................................................................................. 38 Linear Spaces ......................................................................... 41 Fields ................................................................................................... 41 Definition and Properties ..................................................................... 42 Subspaces ........................................................................................... 43 Linear Combinations and Span ........................................................... 43 Linear Independence, Dimension, and Basis ...................................... 44 Linear Mappings ..................................................................... 45 Mappings in General ........................................................................... 45 Linear Mappings .................................................................................. 47 Matrix Representation of Linear Mappings .......................................... 49 Cramer’s Rule...................................................................................... 50