书籍详情
线性代数：英文版
作者：（美）Steven J.Leon著
出版社：机械工业出版社
出版时间：2004-10-01
ISBN：9787111152163
定价：¥59.00
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内容简介
随着计算机技术的发展，线性代数课程的重要性越来越突出。同时，现代软件已经使显著改善授课方式成为可能。《经典原版书库：线性代数（英文版·第6版）》作者多年讲授线性代数课程，并在教学过程中不断探索更利于学生理解的新教学方法，从而使《经典原版书库：线性代数（英文版·第6版）》更加适合作为线性代数课程的教材。《经典原版书库：线性代数（英文版·第6版）》主要包括矩阵与方程组、行列式、向量空间、线性变换、正交性、特征值、迭代法和若尔当标准型等内容。《经典原版书库：线性代数（英文版·第6版）》的主要特点：●通过大量的实际应用说明了线性代数在各个领域中的广泛应用。●包含许多示例，便于读者理解相关的定义及原理。●每一节的后面给出大量的习题，各章后面还有测试题，并在《经典原版书库：线性代数（英文版·第6版）》的最后提供了部分习题的答案。●每章的后面都有基子MALAB的上机练习，并在附录中提供了MALAB的基础知识。
作者简介
StevenJ.Leon1971年于密歇根州大学数学系获得博士学位。现为马萨诸塞大学达特茅斯分校数学系首席教授，ILAS、MAA和SIAM成员。他主要从事科学计算、线性代数和应用数学等领域的研究。
目录
PREFACE iv
1 MATRICES AND SYSTEMS OF EQUATIONS
1 Systems of Linear Equations 1
2 Row Echelon Form 13
3 Matrix Algebra 33
4 Elementary Matrices 67
5 Partitioned Matrices 79
MATLAB Exercises 91
Chapter Test 97
2 DETERMINANTS 99
1 The Determinant ora Matrix 99
2 Properties of Determinants 107
3 Cramer's Rule 115
MATLAB Exercises 121
Chapter Test 123
3 VECTOR-SPACES 125
1 Definition and Examples 125
2 Subspaces 134
3 Linear Independence 144
4 Basis and Dimension 156
5 Change of Basis 163
6 Row Space and Column Space 174
MATLAB Exercises 184
Chapter Test 186
4 LINEAR TRANSFORMATIONS 188
1 Definition and Examples 188
2 Matrix Representations of Linear Transformations 198
3 Similarity 212
MATLAB Exercises 220
Chapter Test 221
5 ORTHOGONALITY 223
1 The Scalar Product in Rn 224
2 Orthogonal Subspaces 239
3 Least Squares Problems 249
4 Inner Product Spaces 260
5 Orthonormal Sets 270
6 The Gram-Schmidt Orthogonalization Process 290
7 Orthogonal Polynomials 299
MATLAB Exercises 307
Chapter Test 310
6 EIGENVALUES 312
1 Eigenvalues and Eigenvectors 313
2 Systems of Linear Differential Equations 326
3 Diagonalization 339
4 Hermitian Matrices 355
5 The Singular Value Decomposition 367
6 Quadratic Forms 382
7 Positive Definite Matrices 397
8 Nonnegative Matrices 405
MATLAB Exercises 412
Chapter Test 421
7 NUMERICAL LINEAR ALGEBRA 422
1 Floating-Point Numbers 423
2 Gaussian Elimination 427
3 Pivoting Strategies 436
4 Matrix Norms and Condition Numbers 442
5 Orthogonal Transformations 458
6 The Eigenvalue Problem 470
7 Least Squares Problems 482
MATLAB Exercises 494
Chapter Test 503
ITERATIVE METHODS *Web
9 JORDAN CANONICAL FORM *Web
APPENDIX: MATLAB 505
BIBLIOGRAPHY 517
ANSWERS TO SELECTED EXERCISES 520
INDEX 540
1 MATRICES AND SYSTEMS OF EQUATIONS
1 Systems of Linear Equations 1
2 Row Echelon Form 13
3 Matrix Algebra 33
4 Elementary Matrices 67
5 Partitioned Matrices 79
MATLAB Exercises 91
Chapter Test 97
2 DETERMINANTS 99
1 The Determinant ora Matrix 99
2 Properties of Determinants 107
3 Cramer's Rule 115
MATLAB Exercises 121
Chapter Test 123
3 VECTOR-SPACES 125
1 Definition and Examples 125
2 Subspaces 134
3 Linear Independence 144
4 Basis and Dimension 156
5 Change of Basis 163
6 Row Space and Column Space 174
MATLAB Exercises 184
Chapter Test 186
4 LINEAR TRANSFORMATIONS 188
1 Definition and Examples 188
2 Matrix Representations of Linear Transformations 198
3 Similarity 212
MATLAB Exercises 220
Chapter Test 221
5 ORTHOGONALITY 223
1 The Scalar Product in Rn 224
2 Orthogonal Subspaces 239
3 Least Squares Problems 249
4 Inner Product Spaces 260
5 Orthonormal Sets 270
6 The Gram-Schmidt Orthogonalization Process 290
7 Orthogonal Polynomials 299
MATLAB Exercises 307
Chapter Test 310
6 EIGENVALUES 312
1 Eigenvalues and Eigenvectors 313
2 Systems of Linear Differential Equations 326
3 Diagonalization 339
4 Hermitian Matrices 355
5 The Singular Value Decomposition 367
6 Quadratic Forms 382
7 Positive Definite Matrices 397
8 Nonnegative Matrices 405
MATLAB Exercises 412
Chapter Test 421
7 NUMERICAL LINEAR ALGEBRA 422
1 Floating-Point Numbers 423
2 Gaussian Elimination 427
3 Pivoting Strategies 436
4 Matrix Norms and Condition Numbers 442
5 Orthogonal Transformations 458
6 The Eigenvalue Problem 470
7 Least Squares Problems 482
MATLAB Exercises 494
Chapter Test 503
ITERATIVE METHODS *Web
9 JORDAN CANONICAL FORM *Web
APPENDIX: MATLAB 505
BIBLIOGRAPHY 517
ANSWERS TO SELECTED EXERCISES 520
INDEX 540
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