《linear algebra》是2019年8月北京郵電大學出版社有限公司出版的圖書，作者是北京郵電大學雙語線性代數教研組，本書可作為高等工科院校線性代數課程雙語教學的教材，也可作為科技工作者的參考書。
基本介紹
- 書名：linear algebra
- 作者：北京郵電大學雙語線性代數教研組
- 出版社：北京郵電大學出版社有限公司
- 出版時間：2019年
- 國際標準書號ISBN：9787563554607
內容簡介,圖書目錄,
內容簡介
本書主要介紹與線性代數相關的基本概念，包括線性代數方程組及其矩陣表示法、矩陣相關運算、向量空間的基本概念、空間解析幾何的基本知識、線性變換的基本概念、內積空間及正交性的基本知識、矩陣的對角化等內容。本書可作為高等工科院校線性代數課程雙語教學的教材，也可作為科技工作者的參考書。
圖書目錄
Chapter 1 Equation Systems and Matrices 1
1.1 Systems of Linear Equations 1
1.1.1 Brief History of Algebra and Linear Algebra 1
1.1.2 Systems of Linear Equations 2
1.1.3 Strict Triangular Form of Linear Systems 7
1.2 Linear System in Matrix 101.2.1 Matrix Notations 10
1.2.2 Solving Linear Systems 111.3 Reduced Row Echelon Form 15
1.3.1 Row Echelon Form 151.3.2 Gauss Elimination 18
1.3.3 Reduced Row Echelon 21
1.4 Consistency of Linear Systems 23
1.4.1 Overdetermined Systems 23
1.4.2 Underdetermined Systems 27
1.4.3 Homogeneous Systems 28
Chapter 2 Matrix Algebra 30
2.1 Notations and Operations 30
2.1.1 Matrix Notations 30
2.1.2 Matrix Operations 31
2.1.3 Algebraic Rules of Matrix Operations 34
2.2 Inverse and Transpose of Matrices 38
2.2.1 Identity Matrix 382.2.2 Matrix Inverse 39
2.2.3 The Transpose of a Matrix 41
2.2.4 Triangular and Diagonal Matrices 42
2.3 Partitioned Matrices 44
2.3.1 The Notations of Partitioned Matrices 44
2.3.2 Block Addition and Scalar Multiplication 46
2.3.3 Block Multiplication 47
2.4 Linear Combination of Vectors 52
2.4.1 Linear Combination of Vectors 52
2.4.2 Equivalent Systems 53
2.4.3 Elementary Matrices 55
2.4.4 Find the Inverse Matrix.59
2.5 The Determinant of a Matrix 61
2.5.1 CASE Ⅰ The Determinant of 1 ￡ 1 Matrices 62
2.5.2 CASE Ⅱ The Determinant of 2 ￡ 2 Matrices 62
2.5.3 CASE Ⅲ 3 ￡ 3 Matrices 63
2.5.4 CASE Ⅳ The Determinant of n ￡ n Matrices 64
2.6 Properties of Determinants 67
2.6.1 Determinant of the Transposed Matrix 67
2.6.2 Determinant of Triangular Matrices.68
2.6.3 Determinant of Matrices with All Zeros in a Row or Column 68
2.6.4 Determinant of Matrices with Identical Rows or Columns 69
2.6.5 ¤Laplace's Deˉnition of Determinant by Using Subdeterminant 70
2.6.6 Algebraic Rules of Determinants 71
2.6.7 Determinant and Singularity of a Matrix 83
2.7 Cramer's Rule 852.7.1 The Adjoint of a Matrix 85
2.7.2 Cramer's Rule 86Chapter 3 Vector Spaces 89
3.1 Deˉnitions and Examples 893.1.1 Definitions 89
3.1.2 Examples 90
3.1.3 Euclidean Vector Space 91
3.1.4 Inner Produc
