Linear Algebra and Matrix Theory / Edition 2

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Intended for a serious first course or a second course in linear algebra, this book carries students beyond eigenvalues and eigenvectors to the classification of bilinear forms, normal matrices, spectral decompositions, the Jordan form, and sequences and series of matrices. The authors present the material from a structural point of view: fundamental algebraic properties of the entities involved are emphasized. The approach is particularly important because the mathematical systems encountered in linear algebra furnish a wealth of examples for the structures studied in more advanced courses. By taking a straight and smooth path to the heart of linear algebra, students will be able to make the transition from the intuitive developments of courses at a lower level to the more abstract treatments encountered later.

Audience: Undergraduate math majors who have some background in linear algebra and would benefit from a strong foundation for more abstract treatments at a higher level. Also serves as text for introductory courses.

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Editorial Reviews

From the Publisher
"Jimmie and Linda Gilbert...present material at the appropriate level in a quick and concise manner....Some texts do not develop enough mathematical sophistication to enable the transition to junior- or senior-level linear algebra courses. The Gilbert text does!" "While the earlier edition of the Gilbert book was suitable for second and third year mathematics students, the level of writing was challenging for first year students. I was very pleased to find that the Gilberts have added a good number of meaningful examples and exercises at the appropriate level for such students. Moreover, in carefully doing so, they have not destroyed their crisp and efficient style of writing."

"I am...quite enthusiastic about the arrangement of topics which the Gilberts have chosen....The Gilberts Chapter 1 plays as a sort of overture, in which the main elements of vector space theory are laid out in a comfortable space, while due attention is paid to the role of computation. I think this type of start to a course would orient the students properly toward general vector space theory, rather than having them come upon the annoying complication of vector spaces after three or more weeks spent exclusively in computation and row reduction."

"The notation and terminology are clear and concise and the flow of topics and concepts is smooth."

"The material is well-written, it will be easy to teach from, and the students will find it easy to read and study from."

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Product Details

  • ISBN-13: 9780122829703
  • Publisher: Elsevier Science & Technology Books
  • Publication date: 5/28/1995
  • Edition description: REPRINT
  • Edition number: 2
  • Pages: 394
  • Product dimensions: 7.74 (w) x 9.53 (h) x 1.01 (d)

Meet the Author

Jimmie Gilbert was Professor of Mathematics at the University of South Carolina, Upstate. He received his Ph.D from Auburn University with a specialty in Linear and Abstract Algebras. He authored the first edition of Elements of Modern Algebra in 1970, joined on subsequent editions by his wife and longtime co-author Linda Gilbert. Together they have published titles in College Algebra, Precalculus, College Algebra and Trigonometry, Trigonometry, Intermediate Algebra, and another Cengage Learning title, Linear Algebra and Matrix Theory, now in its second edition. He and Linda have 6 children and 8 grandchildren. In his leisure time Jimmie enjoyed the outdoors, fishing, and gardening.

Linda Gilbert received her Ph.D. from Louisiana Tech University with a specialty in Linear and Abstract Algebras. She has been writing textbooks since 1981 with her husband Jimmie Gilbert, including ELEMENTS OF MODERN ALGEBRA and LINEAR ALGEBRA and MATRIX THEORY (now in its second edition) with Cengage Learning, plus titles in College Algebra, Precalculus, College Algebra and Trigonometry, Trigonometry, and Intermediate Algebra.

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Table of Contents

1 Real Coordinate Spaces 1
2 Elementary Operations on Vectors 41
3 Matrix Multiplication 59
4 Vector Spaces, Matrices, and Linear Equations 113
5 Linear Transformations 145
6 Determinants 187
7 Eigenvalues and Eigenvectors 213
8 Functions of Vectors 239
9 Inner Product Spaces 293
10 Spectral Decompositions 325
Answers to Selected Exercises 363
Index 389
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