出版時間:2007-5 出版社:機械工業(yè) 作者:里昂 頁數:523
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內容概要
隨著計算機技術的發(fā)展,線性代數課程的重要性越來越突出。同時,現代軟件技術已經為顯著改進授課方式提供了可能。本書作者多年講授線性代數課程,并在教學過程中不斷探索更利于學生理解的新教學方法,從而使本書更加適合作為線性代數課程的教材。 本書主要特點: ·理論與應用有機結合。大量的實際應用貫穿于理論講解的始終,體現了線性代數在各個領域中的廣泛應用?! な纠S富。便于讀者理解相關的定義及原理,增強了讀者學習的興趣?! ち曨}安排科學合理。每一節(jié)的后面給出大量的習題,各章后面還有測試題,使學生有更多的演練機會,達到觸類旁通的效果?! ぞo密結合數學工具MATLAB。每章的后面都有基于MALAB的上機練習,并在附錄中介紹了MALAB的基本用法。
作者簡介
Steven J.Leon,1971年于密歇根州立大學數學系獲得博士學位,現為馬薩諸塞大學達特茅斯分校數學系首席教授,ILAS(國際線性代數協會)、MAA(美國數學學會)和SIAM(美國工業(yè)與應用數學協會)成員。他主要從事科學計算、線性代數和應用數學等領域的研究。
書籍目錄
PREFACE 1 MATRICES AND SYSTEMS OF EQUATIONS 1 Systems of Linear Equations 2 Row Echelon Form 3 Matrix Algebra 4 Elementary Matrices S 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 Iinear 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 B5 ORTHOGONALIT 1 The Scalar Product in Rn 2 Orthogonal Subspaces 3 Least Squares Problems 4 Inner Product Spaces 5 Orthonormal Sets 6 The GramSchmidt 0rthogonalization 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 6 Quadratic Forms 7 Positive Definite Matrices 8 Nonnegative Matrices MATLAB Exercises Chapter Test A Chapter Test B 7 NUMERICAL LINEAR ALGEBRA 1 FloatingPoint 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 METHODS9 CANONICAL FORMSAPPENDIX: MATLAB BIBLIOGRAPHY ANSWERS TO SELECTED EXERCISES INDEX
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