 Linear Algebra with Applications, 8/E
 ISBN10: 0136009298 • ISBN13: 9780136009290
 ©2010 • Pearson • Cloth, 552 pp

Published 08/26/2009 • Instock
http://www.pearsonhighered.com/leon
This book is for sophomorelevel or junior/seniorlevel first courses in linear algebra and assumes calculus as a prerequisite.
This thorough and accessible text, from one of the leading figures in the use of technology in linear algebra, gives students a challenging and broad understanding of the subject. The author infuses key concepts with their modern practical applications to offer students examples of how mathematics is used in the real world. Each chapter contains integrated worked examples and chapter tests. The book stresses the important roles geometry and visualization play in understanding linear algebra.
1. New Section on Matrix Arithmetic
One of the longer sections in the previous edition was the section on matrix algebra in Chapter 1. The material in that section has been expanded further for the current edition. Rather than include an overly long revised section, we have divided the material into sections titled Matrix Arithmetic and Matrix Algebra.
2. New Exercises
After seven editions it was quite a challenge to come up with additional original exercises. This eighth edition has more than 130 new exercises. The new exercises are not evenly distributed throughout the book. Some sections have many new exercises and others have few or none.
3. New Subsections and Applications
A new subsection on cross products has been included in Section 3 of Chapter 2. A new application to Newtonian Mechanics has also been added to that section. In Section 4 of Chapter 6 (Hermitian Matrices), a new subsection on the Real Schur Decomposition has been added.
4. New and Improved Notation
The standard notation for the jth column vector of a matrix A is a_{j} , however, there seems to be no universally accepted notation for row vectors. In the MATLAB package, the ith row of A is denoted by A(i, :). In previous editions of this book we used a similar notation a(i, :), however, this notation seems somewhat artificial. For this edition we use the same notations as for a column vector except we put a horizontal arrow above the letter to indicate that the vector is a row vector (an horizontal array) rather than a column vector (a vertical array).
We have also introduced improved notation for the standard Euclidean vector spaces and their complex counterparts.
5. Other Revisions
Various other revisions have been made throughout the text. Many of these revisions were suggested by reviewers.
6. Special Web Site and Supplemental Web Materials
Pearson has developed a special Web site to accompany the 8th edition. This site includes a host of materials for both students and instructors.
Preface
What’s New in the Eighth Edition?
Computer Exercises
Overview of Text
Suggested Course Outlines
Supplementary Materials
Acknowledgments
1. Matrices and Systems of Equations
1.1 Systems of Linear Equations
1.2 Row Echelon Form
1.3 Matrix Arithmetic
1.4 Matrix Algebra
1.5 Elementary Matrices
1.6 Partitioned Matrices
Matlab Exercises
Chapter Test A
Chapter Test B
2. Determinants
2.1 The Determinant of a Matrix
2.2 Properties of Determinants
2.3 Additional Topics and Applications
Matlab Exercises
Chapter Test A
Chapter Test B
3. Vector Spaces
3.1 Definition and Examples
3.2 Subspaces
3.3 Linear Independence
3.4 Basis and Dimension
3.5 Change of Basis
3.6 Row Space and Column Space
Matlab Exercises
Chapter Test A
Chapter Test B
4. Linear Transformations
4.1 Definition and Examples
4.2 Matrix Representations of Linear Transformations
4.3 Similarity
Matlab Exercises
Chapter Test A
Chapter Test B
5. Orthogonality
5.1 The Scalar Product in R^{n}
5.2 Orthogonal Subspaces
5.3 Least Squares Problems
5.4 Inner Product Spaces
5.5 Orthonormal Sets
5.6 The Gram—Schmidt Orthogonalization Process
5.7 Orthogonal Polynomials
Matlab Exercises
Chapter Test A
Chapter Test B
6. Eigenvalues
6.1 Eigenvalues and Eigenvectors
6.2 Systems of Linear Differential Equations
6.3 Diagonalization
6.4 Hermitian Matrices
6.5 The Singular Value Decomposition
6.6 Quadratic Forms
6.7 Positive Definite Matrices
6.8 Nonnegative Matrices
Matlab Exercises
Chapter Test A
Chapter Test B
7. Numerical Linear Algebra
7.1 FloatingPoint Numbers
7.2 Gaussian Elimination
7.3 Pivoting Strategies
7.4 Matrix Norms and Condition Numbers
7.5 Orthogonal Transformations
7.6 The Eigenvalue Problem
7.7 Least Squares Problems
Matlab Exercises
Chapter Test A
Chapter Test B
Appendix: MATLAB
The MATLAB Desktop Display
Basic Data Elements
Submatrices
Generating Matrices
Matrix Arithmetic
MATLAB Functions
Programming Features
Mfiles
Relational and Logical Operators
Columnwise Array Operators
Graphics
Symbolic Toolbox
Help Facility
Conclusions
Bibliography
A. Linear Algebra and Matrix Theory
B. Applied and Numerical Linear Algebra
C. Books of Related Interest
Answers to Selected Exercises
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