線性代數─精要與解析 (Linear Algebra)

Description

線性代數在各方面的廣大使用使得線性代數課程成為數學、電腦、工程以及商科等各科系的重要課程。本書之設計為一年級之課程，其內容包含定義、定理及證明，而大量的例子 更是本書的特色之一，尤其以每章節後面的例子更可用於複習各章的重點及準備考試用。本書以淺顯之英文來編寫，有別於一般國外原文書之艱澀文法

 

Table of contents

Ch1 MATRICES AND VECTORS
1-1 Matrices and Matrix Operation
1-2 Matrix Inverse;Rules of Matrix Arithmetic
1-3 Norm(Length)and Dot Product
1-4 Cross Product

Ch2 GENERAL VECTOR SPACES
2-1 Real Vector Spaces
2-2 Subspaces
2-3 Linear Combination and Systems of Linear Equations
2-4 Linear Dependence and Linear Independence
2-5 Basis and Dimension

Ch3 LINEAR TRANSFORMATIONS
3-1 Linear Transformations
3-2 Range,Kernel,Rank and Nullity
3-3 Matrices of General Linear Transformations
3-4 Composition of Linear Transformation and Matrix Multiplication
3-5 Invertibillity and Isomorphisms
3-6 The Change of Coordinate Matrix

Ch4 ELEMENTARY MATRIX
4-1 Introduction to Systems of Linear Equations
4-2 Gaussian Elimination
4-3 Elementary Matrix and Elementary Operations

Ch5 DETERMINANTS
5-1 Definition of Determinant in Permutation(Option)
5-2 Determinants of 2*2 Matrix
5-3 Definition and Properties of the Determinant
5-4 Theorem Proof of Determinant
5-5 Cramer`s Rule

Ch6 INNER PRODUCT SPACES
6-1 Inner Product Space
6-2 Angle and Orthogonality in Inner Product Spaces
6-3 Orthonormal Bases;Gram-Schmidt Process;QR-Decomposition
6-4 Best Approximation:(Least Square Method)
6-5 Orthogonal Matrices

Ch7 EIGENVALUES,EIGENVECTORS
7-1 Eigenvalues and Elgenvectors
7-2 Diagonalization
7-3 Orthogonal Diagonalization

Ch8 QUADRATIC FORMS
8-1 Quadratic Forms
8-2 Diagonalizing Quadratic Forma;(Conic Sections)
8-3 Quadric Surfaces

Ch9 CANONICAL FORM
9-1 Jordan Canonical Form