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Linear Algebra with Applications, 7/E
Steven J. Leon

ISBN-10: 0131857851
ISBN-13: 9780131857858

Publisher: Prentice Hall
Copyright: 2006
Format: Cloth; 544 pp
Published: 06/06/2005

Suggested retail price: $141.33
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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.

• Extensive Application of linear algebra concepts to a variety of real world situations – Applications can be used to motivate new material and to show relevance of the material covered.

– Students can easily see what an important tool linear algebra is for solving applied problems.

– See sections 1.3, 5.1, 6.3, and 6.5.

 

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

– Help students to visualize and discover linear algebra and allow them to explore more realistic applications that are too computationally intensive to work out by hand.

– Provides students with experience in performing matrix computations.

– See the MATLAB section in chapter 6.

 

• Worked out examples make the textbook seem less abstract and more user friendly.

– Enhance student understanding of new concepts.

– See section 1.3 which includes 16 worked out examples illustrating every new concept introduced in that section.

 

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

– Reinforce course material in the chapter.

– Serves as a wake-up call for students to focus on what material they have yet to master so they can improve their weaknesses.

– See the two chapter tests at the end of chapter 1.

• New and expanded applications – Interesting and current examples including the application of linear transformations to an airplane, eigenvectors determining the orientation of a space shuttle, and how Google© makes use of linear algebra to rank and order search results.

– Students understand how theories and fundamental linear algebra concepts can help solve modern day problems.

 

• Additional chapter tests and new exercises – A second chapter test with 10 to 12 workout problems has been added to each chapter along with the addition of many new exercises to the exercise sections of the book.

– Aids student self-study and preparation for exams.

 

• Additional new figures

– The addition of seven new figures enhance student visualization of the subject.

 

• MATLAB updates

– The MATLAB appendix has been updated and expanded.  All MATLAB exercises in the book have been checked for compatibility with MATLAB 7.0 (the latest version of MATLAB).  Two MATLAB exercises have been replaced with new exercises.

• A series of MATLAB and Maple guides are FREE when shrink-wrapped with the text.

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. On the website, as pdfs.

 

9. Jordan Canonical Form. On the website, as pdfs.

 

Appendix: MATLAB.

 

Bibliography.

 

Answers to Selected Exercises.

 

Index.

View a Sample Chapter PDF:

 

Revised Study Guide Pages

Page 56
Page 94

For Introductory Linear Algebra


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