出版時(shí)間:2007-5 出版社:機(jī)械工業(yè) 作者:里昂 頁數(shù):523
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內(nèi)容概要
隨著計(jì)算機(jī)技術(shù)的發(fā)展,線性代數(shù)課程的重要性越來越突出。同時(shí),現(xiàn)代軟件技術(shù)已經(jīng)為顯著改進(jìn)授課方式提供了可能。本書作者多年講授線性代數(shù)課程,并在教學(xué)過程中不斷探索更利于學(xué)生理解的新教學(xué)方法,從而使本書更加適合作為線性代數(shù)課程的教材。 本書主要特點(diǎn): ·理論與應(yīng)用有機(jī)結(jié)合。大量的實(shí)際應(yīng)用貫穿于理論講解的始終,體現(xiàn)了線性代數(shù)在各個(gè)領(lǐng)域中的廣泛應(yīng)用?! な纠S富。便于讀者理解相關(guān)的定義及原理,增強(qiáng)了讀者學(xué)習(xí)的興趣?! ち?xí)題安排科學(xué)合理。每一節(jié)的后面給出大量的習(xí)題,各章后面還有測試題,使學(xué)生有更多的演練機(jī)會(huì),達(dá)到觸類旁通的效果?! ぞo密結(jié)合數(shù)學(xué)工具M(jìn)ATLAB。每章的后面都有基于MALAB的上機(jī)練習(xí),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(xué)數(shù)學(xué)系獲得博士學(xué)位,現(xiàn)為馬薩諸塞大學(xué)達(dá)特茅斯分校數(shù)學(xué)系首席教授,ILAS(國際線性代數(shù)協(xié)會(huì))、MAA(美國數(shù)學(xué)學(xué)會(huì))和SIAM(美國工業(yè)與應(yīng)用數(shù)學(xué)協(xié)會(huì))成員。他主要從事科學(xué)計(jì)算、線性代數(shù)和應(yīng)用數(shù)學(xué)等領(lǐng)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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