线性代数
2003-12
高等教育
刘金宪
179
220000
本书是教育科学“十五”国家规划课题研究成果,对线性代数的内容做了较准确的、深入浅出的英文表述。内容包括行列式、矩阵、向量、方程组解的结构、矩阵的特征值与特征向量等。数学专业技术符号系统与国内现行教学规范一致。分节配备了习题并附有答案。本书适合作为高等院校同名课程双语教学的配套教材,也可以作为英语专业数学课程的教科书,以及数学与应用数学、信息与计算科学专业学科英语的阅读读物。
CHAPTER Ⅰ DETERMINANTS Determinants of Order 2 and 3 1.1 Determinants of order 2 1.2 Determinants of order 3 1.3 Exercises Determinants of Order n 2.1" Defining by numbers of inverted sequence 2.2 Defining by induction 2.3 Exercises Properties of Determinants 3.1 Properties of determinants 3.2 Examples 3.3 Exercises Cramer' s Rule 4.1 Background 4.2 Cramer's rule 4.3 ExercisesCHAPTER Ⅱ MATRICES Definition of Matrices 1.1 Definition of a matrix 1.2 Determinant of a square matrix 1.3 Transpose of a matrix 1.4 Exercises Addition and Multiplication by a Number 2.1 Addition of matrices 2.2 Multiplication of a matrix by a number 2.3 Calculation rules 2.4 Exercises 3 Multiplication of Matrices 3.1 Definition of multiplication 3.2 Calculation rules 3.3 Unit matrix 3.4 Powers of square matrices 3.5 Exercises 4 Inverse of a Matrix 4.1 Inverse of a matrix of order 2 4.2 Inverse of an n x n matrix 4.3 Properties of inverse matrices 4.4 Exercises 5 Elementary Operations of a Matrix 5.1 Definition of elementary operations 5.2 Standard form of a matrix 5.3 Elementary square matrix 5.4 Find inverse matrices by elementary operations ~ 5.5 Exercises 6 Rank of a Matrix 6.1 Subdeterminants of a matrix 6.2 Definition of rank of a matrix 6.3 Rank and elementary operations 6.4 Examples 6.5 Exercises 7 Elementary Operations and Elimination 7.1 Representation of equations by matrices 7.2 Elimination in simple cases 7.3 The general case of elimination ……CHAPTER Ⅲ VECTORSCHAPTER Ⅳ STRUCTURE OF SOLUTIONS FOR EQUATIONSCHAPTER Ⅴ EIGENVALUESANSWERS TO EXERCISESINDEXREFERENCES