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彭国华,李德琅 著
出版社: 高等教育出版社 ISBN:9787040192827 版次:1 商品编码:10493326 包装:平装 开本:16开 出版时间:2006-05-01 页数:355 正文语种:中文,英文
1.1 Integers
1.2 Number Fields
1.3 Polynomial
1.4 Polynomial Functions and Roots
1.5 Polvnomials over Rational Number Field
1.6 Polynomials of Several Variables
1.7 Symmetric Polynomials
1.8 Exercises
2 Systems of Linear Equations
2.1 Systems of Linear Equations and Elimination
2.2 Vectors
2.3 Matrices
2.4 Structure of Solutions of A System of Linear Equations
2.5 Exercises
3 Linear Maps, Matrices and Determinants
3. 1 Linear Maps of Vector Spaces and Matrices
3.2 Operations of Linear Maps and Matrices
3.3 Partitioned Matrices
3, 4 Elementary Matrices and Invertible Matrices
3.5 Determinants
3.5.1 Permutation and Determinant
3.5.2 Properties of Determinant
3.5.3 Expansion of Determinant
3.5.4 Applications of Determinant
3.6 Exercises
4 Linear Spaces and Linear Maps
4. 1 Linear Spaces
4.2 Dimension, Basis, Coordinates
4.3 Basis Change and Coordinate Transformations
4.4 Linear Maps and Isomorphism
4.5 Matrices of Linear Maps
4.6 Subspaces and Direct Sum
4.7 Space Decomposition and Partitioned Matrices
4.8 Exercises
5 Linear Transformations
5.1 Linear Transformations
5.2 Similarity of Matrices
5.3 ),-Matrices
5.4 Eigenvalues, Eigenvectors and Characteristic Polynomials
5.5 Invariant Subspaces
5.6 Equivalence of λ-matrices
5.7 Invariant Factors and Elementary Divisors
5.8 Condition for Similarity of Matrices
5.9 Jordan Canonical Forms of Matrices
5.10 Rat iona! Canonical Forms of Matrices
5.11 Exercises
6 Euclidean Spaces
6.1 Inner Product and Basic Properties
6.2 Orthogonal Bases and Schmidt Orthonormalization
6.3 Subspaces and Orthogonal Complements
6.4 Isometry and Orthogonal Transformations
6.5 Symmetric Matrices and Symmetric Transformations
6.6 The Method of Least Squares——System of Linear Equations
Revisited
6.7 A Brief Introduction to Unitary Spaces
6.8 Exercises
7 Linear Forms, Bilinear Forms and Quadratic Forms
7.1 Linear Forms and the Dual Space
7.2 Bilinear Forms
7.3 Symmetric Bilinear Forms
7.4 Quadratic Forms
7.5 Quadratic Forms over Real and Complex Number Fields
7.6 Positive Definite Quadratic Forms over Real Number Field
7.7 Exercises
Bibliography
Index
85.The owner of a rapidly expanding business finds that for the first fivemonths of the year his sales are RMB 4000,4400,5200,6400 and8000.He plots these figures on a graph and conjectures that for the restof the year his sales curve can be approximated by a quadratic polynomia1.Find the least squares quadratic polynomial fit to the sales curve anduse it to project the sales for the 12th month of the year.
86.When the space shuttle Challenger exploded in 1986,one of the criticisms made of NASA’S decision to Launch was in the way the analysis ofnumber of Oring failures versus temperature was made(of course,Oring failure caused the explosion).Four Oring failures will cause therocket tO explode.NASA had data from 24 previous flights.
我们以如何求解线性方程组为出发点,进而考虑解的结构,自然引申出向量、矩阵、行列式、线性空间等概念并展开讨论。第一章预先讨论了一元多项式和多元多项式的基本概念和结论,为后面学习线性代数做准备。在第二章里,我们以讨论解线性方程组的解为中心,引入了向量和矩阵的概念并讨论了它们的基本关系和性质。第三章主要讨论了矩阵的运算和行列式。我们首先建立了在固定的标准单位向量组下向量空间上的线性映射和矩阵的一一对应关系,然后将矩阵的加法和乘积自然定义为线性映射加和乘的矩阵。进而借助映射诱导出矩阵的许多性质。这一章里我们还专门讨论了分块矩阵的运算准则和例子。在讨论行列式时,我们借助初等矩阵,给出矩阵乘积行列式的公式,并没有用到行列式的定义。这些是与大多数的其他同类教材不同的地方。第四章、第五章分别讨论了线性空间、线性映射和线性变换。在第五章里我们还讨论了矩阵、若尔当标准形和一般数域上的有理标准形。第六章是关于欧几里得空间的,主要包含内积空间、正交变换、对称变换、正交矩阵、对称矩阵等基本内容。我们把二次型放到了第七章。这一章先讲了线性型和双线性型。作为应用,我们讨论了二次型和正定二次型的基本性质,包括二次型的标准形问题。
普通高等教育十一五国家级规划教材:linear Algebra 电子书 下载 mobi epub pdf txt
普通高等教育十一五国家级规划教材:linear Algebra-so88
普通高等教育十一五国家级规划教材:linear Algebra pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
||
彭国华,李德琅 著
出版社: 高等教育出版社 ISBN:9787040192827 版次:1 商品编码:10493326 包装:平装 开本:16开 出版时间:2006-05-01 页数:355 正文语种:中文,英文
内容简介
《Linear Algebra》用英语写成,包含多项式和线性代数的基本内容,逻辑清晰,章节安排自然合理,有近550道配套习题,许多习题十分新颖。主要内容包括:整数和多项式,线性方程组,线性映射,矩阵和行列式,线性空间和线性映射,线性变换,欧几里得空间,线性型,双线性型以及二次型。《Linear Algebra》适合数学系本科生作为高等代数教材使用,也可作为双语教学和线性代数的参考教材。目录
1 Integers and Polynomials1.1 Integers
1.2 Number Fields
1.3 Polynomial
1.4 Polynomial Functions and Roots
1.5 Polvnomials over Rational Number Field
1.6 Polynomials of Several Variables
1.7 Symmetric Polynomials
1.8 Exercises
2 Systems of Linear Equations
2.1 Systems of Linear Equations and Elimination
2.2 Vectors
2.3 Matrices
2.4 Structure of Solutions of A System of Linear Equations
2.5 Exercises
3 Linear Maps, Matrices and Determinants
3. 1 Linear Maps of Vector Spaces and Matrices
3.2 Operations of Linear Maps and Matrices
3.3 Partitioned Matrices
3, 4 Elementary Matrices and Invertible Matrices
3.5 Determinants
3.5.1 Permutation and Determinant
3.5.2 Properties of Determinant
3.5.3 Expansion of Determinant
3.5.4 Applications of Determinant
3.6 Exercises
4 Linear Spaces and Linear Maps
4. 1 Linear Spaces
4.2 Dimension, Basis, Coordinates
4.3 Basis Change and Coordinate Transformations
4.4 Linear Maps and Isomorphism
4.5 Matrices of Linear Maps
4.6 Subspaces and Direct Sum
4.7 Space Decomposition and Partitioned Matrices
4.8 Exercises
5 Linear Transformations
5.1 Linear Transformations
5.2 Similarity of Matrices
5.3 ),-Matrices
5.4 Eigenvalues, Eigenvectors and Characteristic Polynomials
5.5 Invariant Subspaces
5.6 Equivalence of λ-matrices
5.7 Invariant Factors and Elementary Divisors
5.8 Condition for Similarity of Matrices
5.9 Jordan Canonical Forms of Matrices
5.10 Rat iona! Canonical Forms of Matrices
5.11 Exercises
6 Euclidean Spaces
6.1 Inner Product and Basic Properties
6.2 Orthogonal Bases and Schmidt Orthonormalization
6.3 Subspaces and Orthogonal Complements
6.4 Isometry and Orthogonal Transformations
6.5 Symmetric Matrices and Symmetric Transformations
6.6 The Method of Least Squares——System of Linear Equations
Revisited
6.7 A Brief Introduction to Unitary Spaces
6.8 Exercises
7 Linear Forms, Bilinear Forms and Quadratic Forms
7.1 Linear Forms and the Dual Space
7.2 Bilinear Forms
7.3 Symmetric Bilinear Forms
7.4 Quadratic Forms
7.5 Quadratic Forms over Real and Complex Number Fields
7.6 Positive Definite Quadratic Forms over Real Number Field
7.7 Exercises
Bibliography
Index
精彩书摘
84.Use the least squares method to find the best choice of a line Y=a。+a1xto fit the(X,Y)一data points(-1,1),(0,0),(1,3),(2,4).Plot the 1ineand the data points in the(x,y)一plane.85.The owner of a rapidly expanding business finds that for the first fivemonths of the year his sales are RMB 4000,4400,5200,6400 and8000.He plots these figures on a graph and conjectures that for the restof the year his sales curve can be approximated by a quadratic polynomia1.Find the least squares quadratic polynomial fit to the sales curve anduse it to project the sales for the 12th month of the year.
86.When the space shuttle Challenger exploded in 1986,one of the criticisms made of NASA’S decision to Launch was in the way the analysis ofnumber of Oring failures versus temperature was made(of course,Oring failure caused the explosion).Four Oring failures will cause therocket tO explode.NASA had data from 24 previous flights.
前言/序言
高等代数是数学系本科一年级的课程。在教学过程中我们逐渐感到有必要编写一本新的高等代数教材。一方面是为了与中学教学内容的衔接,另一方面也是为了顺应时代的需要。由于对课程内容和教学理念有许多一致的看法,两位作者准备联合编写一本高等代数教材。讲义初稿从2000年起着手编写,2001年9月完成,并于当年秋季起一直在四川大学数学学院一年级所有班级中连续使用。由于书稿是在电脑上直接写成的,而敲打汉字对我们来说又是件痛苦的事,因此我们就顺便用英文写成。从近五年的连续使用情况来看,学生反映教材章节安排自然合理,逻辑清晰,举例适当。大多数学生认为习题新颖、量大,难易结合且和教学内容互补搭配。我们以如何求解线性方程组为出发点,进而考虑解的结构,自然引申出向量、矩阵、行列式、线性空间等概念并展开讨论。第一章预先讨论了一元多项式和多元多项式的基本概念和结论,为后面学习线性代数做准备。在第二章里,我们以讨论解线性方程组的解为中心,引入了向量和矩阵的概念并讨论了它们的基本关系和性质。第三章主要讨论了矩阵的运算和行列式。我们首先建立了在固定的标准单位向量组下向量空间上的线性映射和矩阵的一一对应关系,然后将矩阵的加法和乘积自然定义为线性映射加和乘的矩阵。进而借助映射诱导出矩阵的许多性质。这一章里我们还专门讨论了分块矩阵的运算准则和例子。在讨论行列式时,我们借助初等矩阵,给出矩阵乘积行列式的公式,并没有用到行列式的定义。这些是与大多数的其他同类教材不同的地方。第四章、第五章分别讨论了线性空间、线性映射和线性变换。在第五章里我们还讨论了矩阵、若尔当标准形和一般数域上的有理标准形。第六章是关于欧几里得空间的,主要包含内积空间、正交变换、对称变换、正交矩阵、对称矩阵等基本内容。我们把二次型放到了第七章。这一章先讲了线性型和双线性型。作为应用,我们讨论了二次型和正定二次型的基本性质,包括二次型的标准形问题。
普通高等教育十一五国家级规划教材:linear Algebra 电子书 下载 mobi epub pdf txt
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