LINEAR ALGEBRA

定　價(jià)：￥28.00

作　者：	孫曉娟
出版社：	北京郵電大學(xué)出版社
叢編項(xiàng)：
標(biāo)　簽：	暫缺

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ISBN：	9787563555925	出版時(shí)間：	2018-09-01	包裝：
開本：	16開	頁數(shù)：	118	字?jǐn)?shù)：

內(nèi)容簡介

　　《LINEAR ALGEBRA（線性代數(shù) 英文版）/普通高等教育“十三五”規(guī)劃教材》的主要內(nèi)容是矩陣和行列式、線性方程組、方陣的特征值和特征向量、二次型，共四個(gè)章節(jié)。第1章先引入矩陣的概念，而后介紹矩陣的基本運(yùn)算和性質(zhì)、矩陣的秩和逆、方陣的行列式運(yùn)算及其性質(zhì)；第2章介紹線性方程組的解、向量組的線性相關(guān)性、正交基；第3章介紹方陣的特征值與特征向量，以及方陣的相似對角化；最后，第4章介紹二次型及其矩陣和將二次型化為標(biāo)準(zhǔn)型的方法。

作者簡介

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圖書目錄

Chapter 1 Matrices and Determinants
1．1 Matrices
1．2 Matrix Arithmetic
1．2．1 Equality
1．2．2 Scalar Multiplication
1．2．3 Matrix Addition
1．2．4 Matrix Multiplication
1．2．5 Transpose of a Matrix
1．3 Determinants of Square Matrices
1．3．1 Second Order Determinant
1．3．2 n-th Order Determinant
1．3．3 Properties of Determinants
1．3．4 Evaluation of Determinants
1．3．5 Laplace's Theorem
1．4 Block Matrices
1．4．1 The Concept of Block Matrices
1．4．2 Evaluation of Block Matrices
1．5 Invertible Matrices
1．6 Elementary Matrices
1．6．1 Elementary Operations of Matrices
1．6．2 Elementary Matrices
1．6．3 Use Elementary Operations to Get the Inverse Matrix
1．7 Rank of Matrices
1．8 Exercises
Chapter 2 Systems of Linear Equations
2．1 Systems of Linear Equations
2．2 Vectors
2．3 Linear Independence
2．3．1 Linear Combination
2．3．2 Linear Dependence and Linear Independence
2．4 Maximally Linearly Independent Vector Group
2．4．1 Equivalent Vector Sets
2．4．2 Maximally Linearly Independent Group
2．4．3 The Relationship Between Rank of Matrices and Rank of Vector Sets
2．5 Vector Space
2．6 General Solutions of Linear Systems
2．6．1 General Solutions of Homogenous Linear Systems
2．6．2 General Solutions of Non-homogenous Linear Systems
2．7 Exercises
Chapter 3 Eigenvalues and Eigenveetors
3．1 Eigenvalues and Eigenvectors
3．1．1 Definition of Eigenvalues and Eigenvectors
3．1．2 Properties of Eigenvalues and Eigenvectors
3．2 Diagonalization o{ Square Matrices
3．2．1 Similar Matrix
3．2．2 Diagonalization of Square Matrices
3．3 Orthonormal Basis
3．3．1 Inner Product of Vectors
3．3．2 Orthogonal Set and Basis
3．3．3 Gram-Schmidt Orthogonalization Process
3．3．4 Orthogonal Matrix
3．4 Diagonalization of Real Symmetric Matrices
3．4．1 Properties of Eigenvalues of Real Symmetric Matrices
3．5 Exercises
Chapter 4 Quadratic Form
4．1 Real Quadratic Form and Its Matrix
4．2 Diagonal Form of Quadratic Form
4．3 Diagonal Form of Real Quadratic Form
4．3．1 Changing Quadratic Form into Diagonal Form by Orthogonal Transformation
4．3．2 Changing Quadratic Form into Diagonal Form by the Method of Completing the Square
4．4 Canonical Form of Real Quadratic Form
4．5 Positive Definite Quadratic Form and Matrices
4．6 Exercises
References