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Linear Algebra and Matrix Theory - 2nd edition

Linear Algebra and Matrix Theory (ISBN10: 0534405819; ISBN13: 9780534405816)
ISBN13: 978-0534405816
ISBN10: 0534405819

Summary: 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 mathe
matical 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.

Benefits:
  • NEW! Through rewritten material and increased examples and exercises, the pace of the early chapters, especially the first, has been made slower to help students can gain confidence early.
  • NEW! Four new sections appear in Chapters 1 -10, including one on LU decompositions.
  • NEW! A new Chapter 11, "Numerical Methods," enhances the usefulness of the text for two courses.
  • The unifying concept for the first five chapters is that of elementary operations. The concept provides the pivot for a concise and efficient development of the basic theory of vector spaces, linear transformations, matrix multiplication, and the fundamental equivalence relations on matrices.
  • A rigorous treatment of determinants from the traditional viewpoint is presented in Chapter 6.
  • In Chapters 7 - 10, the central theme is the change in the matrix representing a function when only certain types of basis changes are admitted.
  • Numerous examples and exercises illustrate the theory. The exercises are of both theoretical and computational nature. Those of a theoretical nature amplify the treatment and provide experience in constructing deductive arguments, while those of a computational nature illustrate fundamental techniques.
...show more
Summary: 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.

Benefits:
  • NEW! Through rewritten material and increased examples and exercises, the pace of the early chapters, especially the first, has been made slower to help students can gain confidence early.
  • NEW! Four new sections appear in Chapters 1 -10, including one on LU decompositions.
  • NEW! A new Chapter 11, "Numerical Methods," enhances the usefulness of the text for two courses.
  • The unifying concept for the first five chapters is that of elementary operations. The concept provides the pivot for a concise and efficient development of the basic theory of vector spaces, linear transformations, matrix multiplication, and the fundamental equivalence relations on matrices.
  • A rigorous treatment of determinants from the traditional viewpoint is presented in Chapter 6.
  • In Chapters 7 - 10, the central theme is the change in the matrix representing a function when only certain types of basis changes are admitted.
  • Numerous examples and exercises illustrate the theory. The exercises are of both theoretical and computational nature. Those of a theoretical nature amplify the treatment and provide experience in constructing deductive arguments, while those of a computational nature illustrate fundamental techniques.
...show less

Edition/Copyright: 2ND 04
Cover: Hardback
Publisher: Brooks/Cole Publishing Co.
Year Published: 2004
International: No

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