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Linear Algebra with Applications, 6/E
Steven J. Leon, University of Massachusetts, Dartmouth

ISBN-10: 0130337811
ISBN-13: 9780130337818

Publisher: Pearson
Copyright: 2002
Format: Paper; 544 pp
Published: 08/07/2001

Written for undergraduate first courses in Linear Algebra. Assumes the user has had calculus.

Renowned for thoroughness and accessibility, this top-selling text by one of the leading figures in linear algebra education offers students a challenging and enjoyable study of linear algebra that is infused with an abundance of applications. Balancing coverage of mathematical theory and applied topics, Professor Leon explains concepts with precision so that students at any level can understand the material. Worked examples are heavily integrated into each chapter. The book stresses the important role geometry and visualization play in understanding the subject. This edition will continue to be packaged with the ancillary ATLAST computer exercise guide, as well as new MATLAB and Maple guides.

This product accompanies:
Leon, Linear Algebra with Applications, 7/E

NEW - Chapter Tests—At the end of each chapter there is now a true-false exam testing the basic concepts covered in the chapter.
- Asks students to prove or explain their answers.

NEW - Earlier presentation of the Singular Value Decomposition—Now covered in Chapter 6, Section 5 and includes the applications of the singular value decomposition to least square problems, principal component analysis, information retrieval, numerical rank of a matrix, and digital imaging.
- This is one of the most important topics in the course, particularly for students that need to learn to use linear algebra as a tool for solving applied problems. This topic nicely ties together some of the major themes of the course such as fundamental subspaces, orthogonality, and eigenvalues.

NEW - New and improved applications—More applications have been added throughout the book and many of the previous applications have been revised and improved.
- Applications on such topics as search engines and computer graphics widen the audience for linear algebra.

NEW - New and improved examples—More examples have been added throughout the book and many of the previous examples have been revised and improved.
- Worked out examples make the textbook seem less abstract and more user friendly. Now the 32 worked out examples in Chapter 1 of the fifth edition have been increased to 34 examples for the new edition.

NEW - Revised organization of Chapter 5—Least squares problems are now covered before the section on general inner product spaces.
- One of the most important topics in the course is orthogonality — and the book covers this topic in more depth than any competing linear algebra textbook. It is now easier for instructors to cover the most basic and important topics (sections 1 and 2) and then do the main application in section 3 (rather than section 4). They can then skip the more advanced topics in sections 4-7 or defer those topics to a second course in linear algebra.

HALLMARK FEATURES

The most extensive set of chapter-ending computer exercises of any linear algebra text on the market.

Many applications are presented from the start.
- Students can see early on what an important tool linear algebra is for solving applied problems.

The use of geometry is emphasized to visualize linear algebra and aid in understanding all of the major topics.

Carefully designed MATLAB computing exercises included in each chapter—Shed light on the mathematical significance of the computations.
- Provides students with experience in performing matrix computations.

Some of the more difficult vector space concepts are previewed early on, i.e., covers linear combinations right after the definition of matrix multiplication.

Chapter Tests—At the end of each chapter there is now a true-false exam testing the basic concepts covered in the chapter.
- Asks students to prove or explain their answers.

Earlier presentation of the Singular Value Decomposition—Now covered in Chapter 6, Section 5 and includes the applications of the singular value decomposition to least square problems, principal component analysis, information retrieval, numerical rank of a matrix, and digital imaging.
- This is one of the most important topics in the course, particularly for students that need to learn to use linear algebra as a tool for solving applied problems. This topic nicely ties together some of the major themes of the course such as fundamental subspaces, orthogonality, and eigenvalues.

New and improved applications—More applications have been added throughout the book and many of the previous applications have been revised and improved.
- Applications on such topics as search engines and computer graphics widen the audience for linear algebra.

New and improved examples—More examples have been added throughout the book and many of the previous examples have been revised and improved.
- Worked out examples make the textbook seem less abstract and more user friendly. Now the 32 worked out examples in Chapter 1 of the fifth edition have been increased to 34 examples for the new edition.

Revised organization of Chapter 5—Least squares problems are now covered before the section on general inner product spaces.
- One of the most important topics in the course is orthogonality — and the book covers this topic in more depth than any competing linear algebra textbook. It is now easier for instructors to cover the most basic and important topics (sections 1 and 2) and then do the main application in section 3 (rather than section 4). They can then skip the more advanced topics in sections 4-7 or defer those topics to a second course in linear algebra.

(*The Supplemental Chapters 8 and 9 can be downloaded from the web page.)

1. Matrices and Systems of Equations.

Systems of Linear Equations. Row Echelon Form. Matrix Algebra. Elementary Matrices. Partitioned Matrices. Matlab Exercises. Chapter Test.

2. Determinants.

The Determinant of a Matrix. Properties of Determinants. Cramer's Rule. Matlab Exercises. Chapter Test.

3. Vector Spaces.

Definition and Examples. Subspaces. Linear Independence. Basis and Dimension. Change of Basis. Row Space and Column Space. Matlab Exercises. Chapter Test.

4. Linear Transformations.

Definition and Examples. Matrix Representations of Linear Transformations. Similarity. Matlab Exercises. Chapter Test.

5. Orthogonality.

The Scalar Product in Rn. Orthogonal Subspaces. Least Squares Problems. Inner Product Spaces. Orthonormal Sets. The Gram-Schmidt Orthogonalization Process. Orthogonal Polynomials. Matlab Exercises. Chapter Test.

6. Eigenvalues.

Eigenvalues and Eigenvectors. Systems of Linear Differential Equations. Diagonalization. Hermitian Matrices. The Singular Value Decomposition. Quadratic Forms. Positive Definite Matrices. Nonnegative Matrices. Matlab Exercises. Chapter Test.

7. Numerical Linear Algebra.

Floating-Point Numbers. Gaussian Elimination. Pivoting Strategies. Matrix Norms and Condition Numbers. Orthogonal Transformations. The Eigenvalue Problem. Least Squares Problems. Matlab Exercises. Chapter Test.

*8. Iterative Methods.

*9. Jordan Canonical Form.

Appendix: MATLAB.

Bibliography.

Answers to Selected Exercises.

Index.

Introductory Linear Algebra [MORE RIGOROUS FIRST COURSE] (Mathematics)

Linear Algebra with Applications, 7/E
Leon
©2006 | Pearson | Cloth; 544 pp | Out of Stock
ISBN-10: 0131857851 | ISBN-13: 9780131857858
Suggested retail price: $138.67 Net price: $104.00 (What's this?)Brief Description

For sophomore-level or junior/senior-level first courses in Linear Algebra; assumes a Calculus 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 role geometry and visualization play in understanding linear algebra. This edition will continue to be packaged with the ancillary ATLAST computer exercise guide, as well as new MATLAB and Maple guides, which are also free in the package.
Linear Algebra with Applications, 8/E
Leon
©2010 | Pearson | Cloth; 552 pp | Instock
ISBN-10: 0136009298 | ISBN-13: 9780136009290
Net price: $104.00 (What's this?)Brief Description

This book is for sophomore-level or junior/senior-level 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.

Companion Website - Leon, 6/E
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©2002 | Pearson | On-line Supplement | Instock
ISBN-10: 0130337846 | ISBN-13: 9780130337849

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Companion Website - Leon, 6/E
Leon
©2002 | Pearson | On-line Supplement | Instock
ISBN-10: 0130337846 | ISBN-13: 9780130337849

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