
Linear Algebra with Applications
International Edition
Otto Bretscher(Author)
Pearson (Publisher)
5th Edition
Published on 10. January 2013
Book
Paperback/Softback
528 pages
978-0-321-89058-0 (ISBN)
Article exhausted; check for reprint
Description
Offering the most geometric presentation available, Linear Algebra with Applications, Fifth Edition emphasizes linear transformations as a unifying theme. This elegant textbook combines a user-friendly presentation with straightforward, lucid language to clarify and organize the techniques and applications of linear algebra. Exercises and examples make up the heart of the text, with abstract exposition kept to a minimum. Exercise sets are broad and varied and reflect the author's creativity and passion for this course. This revision reflects careful review and appropriate edits throughout, while preserving the order of topics of the previous edition.
More details
Edition
5th edition
Language
English
Place of publication
United States
Publishing group
Pearson Education (US)
Target group
College/higher education
Dimensions
Height: 255 mm
Width: 203 mm
Thickness: 17 mm
Weight
714 gr
ISBN-13
978-0-321-89058-0 (9780321890580)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
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Book
07/2013
5th Edition
Pearson Education Limited
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Book
11/2008
4th Edition
Pearson
€128.74
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Content
1. Linear Equations
1.1 Introduction to Linear Systems
1.2 Matrices, Vectors, and Gauss-Jordan Elimination
1.3 On the Solutions of Linear Systems; Matrix Algebra
2. Linear Transformations
2.1 Introduction to Linear Transformations and Their Inverses
2.2 Linear Transformations in Geometry
2.3 Matrix Products
2.4 The Inverse of a Linear Transformation
3. Subspaces of Rn and Their Dimensions
3.1 Image and Kernel of a Linear Transformation
3.2 Subspace of Rn; Bases and Linear Independence
3.3 The Dimension of a Subspace of Rn
3.4 Coordinates
4. Linear Spaces
4.1 Introduction to Linear Spaces
4.2 Linear Transformations and Isomorphisms
4.3 The Matrix of a Linear Transformation
5. Orthogonality and Least Squares
5.1 Orthogonal Projections and Orthonormal Bases
5.2 Gram-Schmidt Process and QR Factorization
5.3 Orthogonal Transformations and Orthogonal Matrices
5.4 Least Squares and Data Fitting
5.5 Inner Product Spaces
6. Determinants
6.1 Introduction to Determinants
6.2 Properties of the Determinant
6.3 Geometrical Interpretations of the Determinant; Cramer's Rule
7. Eigenvalues and Eigenvectors
7.1 Diagonalization
7.2 Finding the Eigenvalues of a Matrix
7.3 Finding the Eigenvectors of a Matrix
7.4 More on Dynamical Systems
7.5 Complex Eigenvalues
7.6 Stability
8. Symmetric Matrices and Quadratic Forms
8.1 Symmetric Matrices
8.2 Quadratic Forms
8.3 Singular Values
9. Linear Differential Equations
9.1 An Introduction to Continuous Dynamical Systems
9.2 The Complex Case: Euler's Formula
9.3 Linear Differential Operators and Linear Differential Equations
Appendix A. Vectors
Appendix B: Techniques of Proof
Answers to Odd-numbered Exercises
Subject Index
Name Index
1.1 Introduction to Linear Systems
1.2 Matrices, Vectors, and Gauss-Jordan Elimination
1.3 On the Solutions of Linear Systems; Matrix Algebra
2. Linear Transformations
2.1 Introduction to Linear Transformations and Their Inverses
2.2 Linear Transformations in Geometry
2.3 Matrix Products
2.4 The Inverse of a Linear Transformation
3. Subspaces of Rn and Their Dimensions
3.1 Image and Kernel of a Linear Transformation
3.2 Subspace of Rn; Bases and Linear Independence
3.3 The Dimension of a Subspace of Rn
3.4 Coordinates
4. Linear Spaces
4.1 Introduction to Linear Spaces
4.2 Linear Transformations and Isomorphisms
4.3 The Matrix of a Linear Transformation
5. Orthogonality and Least Squares
5.1 Orthogonal Projections and Orthonormal Bases
5.2 Gram-Schmidt Process and QR Factorization
5.3 Orthogonal Transformations and Orthogonal Matrices
5.4 Least Squares and Data Fitting
5.5 Inner Product Spaces
6. Determinants
6.1 Introduction to Determinants
6.2 Properties of the Determinant
6.3 Geometrical Interpretations of the Determinant; Cramer's Rule
7. Eigenvalues and Eigenvectors
7.1 Diagonalization
7.2 Finding the Eigenvalues of a Matrix
7.3 Finding the Eigenvectors of a Matrix
7.4 More on Dynamical Systems
7.5 Complex Eigenvalues
7.6 Stability
8. Symmetric Matrices and Quadratic Forms
8.1 Symmetric Matrices
8.2 Quadratic Forms
8.3 Singular Values
9. Linear Differential Equations
9.1 An Introduction to Continuous Dynamical Systems
9.2 The Complex Case: Euler's Formula
9.3 Linear Differential Operators and Linear Differential Equations
Appendix A. Vectors
Appendix B: Techniques of Proof
Answers to Odd-numbered Exercises
Subject Index
Name Index