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《時代教育國外高校優秀教材精選:綫性代數引論(英文版·原書第5版)》係統新穎、內容豐富、聯係實際、語言通暢,且結閤數學軟件提供瞭一個現代化的學習環境,相對於國內現行教學大綱,教師便於取捨內容組織教學,不失為一本很好的教科書和教學參考書。本書可供理工科、經濟管理各專業學生作為學習綫性代數的教科書或教學參考書,也可供科技人員和自學者參考。
內容簡介
《時代教育國外高校優秀教材精選:綫性代數引論(英文版·原書第5版)》內容覆蓋瞭我國現行理工科大學綫性代數課程的全部內容,與我國現行的綫性代數教學大綱和教材體係比較接近。其中包括矩陣與綫性方程組、二維和三維空間、嚮量空間Rn、特徵值問題、嚮量空間和綫性變換、行列式、特徵值及其應用等。本書的編寫采用模塊式結構,便於廣大教師根據教學需要對內容進行取捨。本書通過例子介紹瞭非常流行的教學軟件Matlab在綫性代數中的應用,並且每章結尾都附有專門用Matlab做的練習題。《時代教育國外高校優秀教材精選:綫性代數引論(英文版·原書第5版)》可供理工科、經濟管理各專業學生作為教科書或參考書。也可供科技人員和自學者參考。
目錄
MATRICES AND SYSTEMS OF LINEAR EQUATIONS
1.1 Introduction to Matrices and Systems of Linear Equatio
1.2 Echelon Form and Gauss-Jordan Elimination
1.3 Co istent Systems of Linear Equatio
1.4 Applicatio (Optional)
1.5 Matrix Operatio
1.6 Algebraic Properties of Matrix Operatio
1.7 Linear Independence and No ingular Matrices
1.8 Data Fitting, Numerical Integration, and Numerical Differentiation (Optional)
1.9 Matrix Inve es and Their Properties
VECTORS IN 2-SPACE AND 3-SPACE
2.1 Vecto in the Plane
2.2 Vecto in Space
2.3 The Dot Product and the Cross Product
2.4 Lines and Planes in Space
THE VECTOR SPACE Rn
3.1 Introduction
3.2 Vector Space Properties of Rn
3.3 Examples of Subspaces
3.4 Bases for Subspaces
3.5 Dime ion
3.6 Orthogonal Bases for Subspaces
3.7 Linear Tra formatio from Rn to Rm
3.8 Least-Squares Solutio to Inco istent Systems, with Applicatio to Data Fitting
3.9 Theory and Practice of Least Squares
THE EIGENVALUE PROBLEM
4.1 The Eigenvalue Problem for (2x2) Matrices
4.2 Determinants and the Eigenvalue Problem
4.3 Elementary Operatio and Determinants (Optional)
4.4 Eigenvalues and the Characteristic Polynomial
4.5 Eigenvecto and Eige paces
4.6 Complex Eigenvalues and Eigenvecto
4.7 Similarity Tra formatio and Diagonalization
4.8 Difference Equatio ; Markov Chai ; Systems of Differential Equatio (Optional)
VECTOR SPACES AND LINEAR TRANSFORMATIONS
5.1 Introduction
5.2 Vector Spaces
5.3 Subspaces
5.4 Linear Independence, Bases, and Coordinates
5.5 Dime ion
5.6 Inner-Product Spaces, Orthogonal Bases, and Projectio (Optional)
5.7 Linear Tra formatio
5.8 Operatio with Linear Tra formatio
5.9 Matrix Representatio for Linear Tra formatio
5.10 Change of Basis and Diagonalization
DETERMINANTS
6.1 Introduction
6.2 Cofactor Expa io of Determinants
6.3 Elementary Operatio and Determinants
6.4 Cramer's Rule
6.5 Applicatio of Determinants: Inve es and Wronksia
EIGENVALUES AND APPLICATIONS
7.1 Quadratic Forms
7.2 Systems of Differential Equatio
7.3 Tra formation to Hessenberg Form
7.4 Eigenvalues of Hessenberg Matrices
7.5 Householder Tra formatio
7.6 The QR Factorization and Least-Squares Solutio
7.7 Matrix Polynomials and the Cayley-Hamilton Theorem
7.8 Generalized Eigenvecto and Solutio of Systems of Differential Equatio
APPENDIX: AN INTRODUCTION TO MATLAB
ANSWERS TO SELECTED ODD-NUMBERED EXERCISES
INDEX
前言/序言
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