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隨著計算機技術的發展，綫性代數課程的重要性越來越突齣。同時，現代軟件技術已經為顯著改進授課方式提供瞭可能。本書作者多年講授綫性代數課程，並在教學過程中不斷探索更利於學生理解的新教學方法，從而使本書更加適閤作為綫性代數課程的教材。

·理論與應用有機結閤。大量的實際應用貫穿於理論講解的始終，體現瞭綫性代數在各個領域中的廣泛應用。

本書主要特點：

·示例豐富。便於讀者理解相關的定義及原理，增強瞭讀者學習的興趣。..

·習題安排科學閤理。每一節的後麵給齣大量的習題，各章後麵還有測試題，使學生有更多的演練機會，達到觸類旁通的效果。

·緊密結閤數學工具MATLAB。每章的後麵都有基於MALAB的上機練習，並在附錄中介紹瞭MALAB的基本用法。

Steven J.Leon，1971年於密歇根州立大學數學係獲得博士學位，現為馬薩諸塞大學達特茅斯分校數學係首席教授，ILAS（國際綫性代數協會）、MAA（美國數學學會）和SIAM（美國工業與應用數學協會）成員。他主要從事科學計算、綫性代數和應用數學等領域的研究。

PREFACE
1 MATRICES AND SYSTEMS OF EQUATIONS
1 Systems of Linear Equations
2 Row Echelon Form
3 Matrix Algebra
4 Elementary Matrices
5 Partitioned Matrices
MATLAB Exercises
Chapter Test A
Chapter Test B
2 DETERMINANTS
1 The Determinant of a Matrix
2 Properties of Determinants
3 Cramer's Rule
MATLAB Exercises
Chapter Test A
Chapter Test B
3 VECTOR SPACES
1 Definition and Examples
2 Subspaces
3 Linear Independence
4 Basis and Dimension
5 Change of Basis
6 Row Space and Column Space
MATLAB Exercises
Chapter Test A
Chapter Test B
4 LINEAR TRANSFORMATIONS
1 Definition and Examples
2 Matrix Representations of Linear Transformations
3 Similarity
MATLAB Exercises
Chapter Test A
Chapter Test B
5 ORTHOGONALITY
1 The Scalar Product in Rn
2 Orthogonal Subspaces
3 Least Squares Problems
4 Inner Product Spaces..
5 Orthonormal Sets
6 The Gram-Schmidt Orthogonalization Process
7 Orthogonal Polynomials
MATLAB Exercises
Chapter Test A
Chapter Test B
6 EIGENVALUES
1 Eigenvalues and Eigenvectors
2 Systems of Linear Differential Equations
3 Diagonalization
4 Hermitian Matrices
5 The Singular Value Decomposition
G Quadratic Forms
7 Positive Definite Matrices
8 Nonnegative Matrices
MATLAB Exercises
Chapter Test A
Chapter Test B
7 NUMERICAL LINEAR ALGEBRA
1 Floating-Point Numbers
2 Gaussian Elimination
3 Pivoting Strategies
4 Matrix Norms and Condition Numbers
5 Orthogonal Transformations
6 The Eigenvalue Problem
7 Least Squares Problems
MATLAB Exercises
Chapter Test A
Chapter Test B
8 ITERATIVE METHODS
9 CANONICAL FORMS
APPENDIX: MATLAB
BIBLIOGRAPHY
ANSWERS TO SELECTED EXERCISES
INDEX
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