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A concise text on advanced linear algebra

By: Publication details: Cambridge University Press 2015 UKDescription: xiii, 318 pISBN:
  • 9781107087514
Subject(s): DDC classification:
  • 512.5 Y2C6
Summary: This engaging textbook for advanced undergraduate students and beginning graduates covers the core subjects in linear algebra. The author motivates the concepts by drawing clear links to applications and other important areas, such as differential topology and quantum mechanics. The book places particular emphasis on integrating ideas from analysis wherever appropriate. For example, the notion of determinant is shown to appear from calculating the index of a vector field which leads to a self-contained proof of the Fundamental Theorem of Algebra, and the Cayley–Hamilton theorem is established by recognizing the fact that the set of complex matrices of distinct eigenvalues is dense. The material is supplemented by a rich collection of over 350 mostly proof-oriented exercises, suitable for students from a wide variety of backgrounds. Selected solutions are provided at the back of the book, making it suitable for self-study as well as for use as a course text. • A well-motivated presentation which avoids unnecessary abstraction to give readers a clear grasp of the concepts covered • Demonstrates connections between linear algebra and other important areas • Contains a diverse range of over 350 exercises, with selected solutions (http://www.cambridge.org/us/academic/subjects/mathematics/algebra/concise-text-advanced-linear-algebra?format=HB)
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Holdings
Item type Current library Item location Collection Shelving location Call number Status Date due Barcode
Books Vikram Sarabhai Library Rack 28-A / Slot 1364 (0 Floor, East Wing) Non-fiction General Stacks 512.5 Y2C6 (Browse shelf(Opens below)) Available 190348

Table of contents:

1. Vector spaces
2. Linear mappings
3. Determinants
4. Scalar products
5. Real quadratic forms and self-adjoint mappings
6. Complex quadratic forms and self-adjoint mappings
7. Jordan decomposition
8. Selected topics
9. Excursion: quantum mechanics in a nutshell

This engaging textbook for advanced undergraduate students and beginning graduates covers the core subjects in linear algebra. The author motivates the concepts by drawing clear links to applications and other important areas, such as differential topology and quantum mechanics. The book places particular emphasis on integrating ideas from analysis wherever appropriate. For example, the notion of determinant is shown to appear from calculating the index of a vector field which leads to a self-contained proof of the Fundamental Theorem of Algebra, and the Cayley–Hamilton theorem is established by recognizing the fact that the set of complex matrices of distinct eigenvalues is dense. The material is supplemented by a rich collection of over 350 mostly proof-oriented exercises, suitable for students from a wide variety of backgrounds. Selected solutions are provided at the back of the book, making it suitable for self-study as well as for use as a course text.
• A well-motivated presentation which avoids unnecessary abstraction to give readers a clear grasp of the concepts covered
• Demonstrates connections between linear algebra and other important areas
• Contains a diverse range of over 350 exercises, with selected solutions

(http://www.cambridge.org/us/academic/subjects/mathematics/algebra/concise-text-advanced-linear-algebra?format=HB)

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