Topics in Quaternion Linear Algebra
eBook - ePub

Topics in Quaternion Linear Algebra

  1. 384 pages
  2. English
  3. ePUB (mobile friendly)
  4. Available on iOS & Android
eBook - ePub

Topics in Quaternion Linear Algebra

About this book

Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations.

Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.

Frequently asked questions

Yes, you can cancel anytime from the Subscription tab in your account settings on the Perlego website. Your subscription will stay active until the end of your current billing period. Learn how to cancel your subscription.
At the moment all of our mobile-responsive ePub books are available to download via the app. Most of our PDFs are also available to download and we're working on making the final remaining ones downloadable now. Learn more here.
Perlego offers two plans: Essential and Complete
  • Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
  • Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Both plans are available with monthly, semester, or annual billing cycles.
We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1 million books across 1000+ topics, we’ve got you covered! Learn more here.
Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more here.
Yes! You can use the Perlego app on both iOS or Android devices to read anytime, anywhere — even offline. Perfect for commutes or when you’re on the go.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access Topics in Quaternion Linear Algebra by Leiba Rodman in PDF and/or ePUB format, as well as other popular books in Mathematics & Computer Science General. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover Page
  2. Title Page
  3. Copyright Page
  4. Dedication Page
  5. Contents
  6. Preface
  7. 1 Introduction
  8. 2 The algebra of quaternions
  9. 3 Vector spaces and matrices: Basic theory
  10. 4 Symmetric matrices and congruence
  11. 5 Invariant subspaces and Jordan form
  12. 6 Invariant neutral and semidefinite subspaces
  13. 7 Smith form and Kronecker canonical form
  14. 8 Pencils of hermitian matrices
  15. 9 Skewhermitian and mixed pencils
  16. 10 Indefinite inner products: Conjugation
  17. 11 Matrix pencils with symmetries: Nonstandard involution
  18. 12 Mixed matrix pencils: Nonstandard involutions
  19. 13 Indefinite inner products: Nonstandard involution
  20. 14 Matrix equations
  21. 15 Appendix: Real and complex canonical forms
  22. Bibliography
  23. Index