Elementary Linear Algebra : A Matrix Approach （2ND）

Spence, Lawrence E./ Insel, Arnold J./ Friedberg, Stephen H.

Pearson College Div（2007/06発売）

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製本 Hardcover:ハードカバー版／ページ数 626 p.
言語 ENG
商品コード 9780131871410
DDC分類 512.5

Full Description

For a sophomore-level course in Linear Algebra.Based on the recommendations of the Linear Algebra Curriculum Study Group, this introduction to linear algebra offers a matrix-oriented approach with more emphasis on problem solving and applications. Throughout the text, use of technology is encouraged. The focus is on matrix arithmetic, systems of linear equations, properties of Euclidean n-space, eigenvalues and eigenvectors, and orthogonality. Although matrix-oriented, the text provides a solid coverage of vector spaces

PREFACE ixTO THE STUDENT xv1.1 Matrices and Vectors 11.2 Linear Combinations, Matrix-Vector Products, and Special Matrices 111.3 Systems of Linear Equations 251.4 Gaussian Elimination 391.5* Applications of Systems of Linear Equations 541.6 The Span of a Set of Vectors 641.7 Linear Dependence and Linear Independence 73Chapter 1 Review ExercisesChapter 1 MATLAB ExercisesCHAPTER 2 MATRICES AND LINEAR TRANSFORMATIONS 902.1 Matrix Multiplication 902.2* Applications of Matrix Multiplication 1012.3 Invertibility and Elementary Matrices 1172.4 The Inverse of a Matrix 1302.5* Partitioned Matrices and Block Multiplication 1412.6* The LU Decomposition of a Matrix 1472.7 Linear Transformations and Matrices 1622.8 Composition and Invertibility of Linear Transformations 175Chapter 2 Review ExercisesChapter 2 MATLAB ExercisesCHAPTER 3 DETERMINANTS 1923.1 Cofactor Expansion 1923.2 Properties of Determinants 204Chapter 3 Review ExercisesChapter 3 MATLAB ExercisesCHAPTER 4 SUBSPACES AND THEIR PROPERTIES 2184.1 Subspaces 2184.2 Basis and Dimension 2324.3 The Dimension of Subspaces Associated with a Matrix 2454.4 Coordinate Systems 2544.5 Matrix Representations of Linear Operators 266Chapter 4 Review ExercisesChapter 4 MATLAB ExercisesCHAPTER 5 EIGENVALUES, EIGENVECTORS, AND DIAGONALIZATION 2825.1 Eigenvalues and Eigenvectors 2825.2 The Characteristic Polynomial 2915.3 Diagonalization of Matrices 3025.4* Diagonalization of Linear Operators 3145.5* Applications of Eigenvalues 323Chapter 5 Review ExercisesChapter 5 MATLAB ExercisesCHAPTER 6 ORTHOGONALITY 3476.1 The Geometry of Vectors 3476.2 Orthogonal Vectors 3606.3 Orthogonal Projections 3746.4 Least-Squares Approximations and Orthogonal Projections 3886.5 Orthogonal Matrices and Operators 3986.6 Symmetric Matrices 4126.7* Singular Value Decomposition 4256.8* Principal Component Analysis 4436.9* Rotations of R3 and Computer Graphics 452Chapter 6 Review ExercisesChapter 6 MATLAB ExercisesCHAPTER 7 VECTOR SPACES 4737.1 Vector Spaces and Their Subspaces 4737.2 Linear Transformations 4857.3 Basis and Dimension 4957.4 Matrix Representations of Linear Operators 5057.5 Inner Product Spaces 517Chapter 7 Review ExercisesChapter 7 MATLAB ExercisesAPPENDICES 534A Sets 534B Functions 536C Complex Numbers 539D Matlab 544E The Uniqueness of the Reduced Row Echelon Form 558REFERENCES 561INDEX 609