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线性代数PDF|Epub|txt|kindle电子书版本网盘下载
- 熊令纯著 著
- 出版社： 北京：原子能出版社
- ISBN：9787502250959
- 出版时间：2010
- 标注页数：141页
- 文件大小：5MB
- 文件页数：148页
- 主题词：线性代数－高等学校－教材－英文
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图书目录
CHAPTER 1 DETERMINANTS1
1.1 2×2 Determinant and 3×3 Determinant1
1.1.1 2×2 Determinant1
1.1.2 3×3 Determinant2
1.2 n×n Determinants2
1.2.1 Permutations and the Number of the Inversions2
1.2.2 n×n Determinants4
1.3 The Properties of the Determinants6
1.4 LAPLACE Expansion of Determinants12
1.4.1 LAPLACE Expansion of Determinants along a Row or a Column12
1.4.2 LAPLACE Expansion of Determinants along k Rows or k Columns17
1.5 Cramer's Rule17
Exercises 1 (A)21
Exercises 1 (B)26
CHAPTER 2 MATRICES28
2.1 Concepts of Matrices28
2.2 Operations of Matrices31
2.2.1 Addtion Operation of Matrices as well as the Multiplication of Scalar and Matrix31
2.2.2 Multiplications of Matrices33
2.2.3 Matrix Transpose38
2.2.4 Power of Square Matrices39
2.3 Some Special Matrices39
2.3.1 Diagonal Matrices39
2.3.2 Scalar Matrices40
2.3.3 Identity Matrices40
2.3.4 Lower-Triangular Matrices40
2.3.5 Upper-Triangular Matrices41
2.3.6 Symmetric Matrices41
2.4 Block-Divided Matrices42
2.5 Invertible Matrices46
2.6 Elementary Operations on Matrices50
2.7 Rank of Matrices57
Exercises 2 (A)60
Exercises 2 (B)66
CHAPTER 3 LINEAR EQUATIONS69
3.1 Gaussian Elimination for Solving Linear Equations69
3.2 Vector Space of n Dimensions79
3.2.1 Vectors and Their Linear Operations79
3.3 Linear Relations of Vectors80
3.3.1 Linear Combinations of Vectors80
3.3.2 Linear Dependence and Linear Independence of Vectors82
3.3.3 Linear Dependence and Linear Combination of Vectors85
3.3.4 Rank of Vectors88
3.4 Solution Structures of Linear Equations92
3.4.1 Solution Structures of Homogeneous Linear Equations92
3.4.2 Solution Structures of Nonhomogeneous Linear Equations96
Exercises 3 (A)98
Exercises 3 (B)101
CHAPTER 4 EIGENVALUES OF MATRICES104
4.1 Eigenvalues and Eigenvectors of Matrices104
4.1.1 Eigenvalues of Matrices104
4.1.2 Fundamental Properties of the Eigenvalues and the Eigenvectors of Matrices106
4.2 Similar Matrices107
4.2.1 Similar Matrices and Their Properties107
4.2.2 Conditions for an n×n Matrix A to be Simiar to a Diagonal Matrix108
4.2.3 The Jordan Canonical Form of Matrices110
4.3 Eigenvalues and Eigenvectors of Real Symmetric Matrices112
4.3.1 Inner Products of Vectors112
4.3.2 Orthogonal Vectors113
4.3.3 Orthogonal Matrices114
4.3.4 Eigenvalues and Eigenvectors of Real Symmetric Matrices115
Exercises 4118
CHAPTER 5 QUADRATIC FORMS120
5.1 Quadratic Forms and Symmetric Matrices120
5.1.1 Quadratic Forms and the Related Symmetric Matrices120
5.1.2 Linear Transformations121
5.2 Normalized Forms Quadratic Forms and Symmetric Matrices124
5.2.1 Normalizing Quadratic Forms and the Related Symmetric Matrices by Completing Squares124
5.2.2 Elementary Operations Used in Deducing Quadratic Forms to Normalized Ones127
5.2.3 Normalizing Quadratic Forms with Orthogonal Linear Transformations128
5.2.4 Normalized Forms of Quadratic Forms and the Corresponding Matrices130
5.3 Quadratic Forms and Definite Matrices131
5.4 An Application of Definite Quadratic Forms137
Exercises 5 (A)139
Exercises 5 (B)140