Square Matrices of Order 2

Theory, Applications, and Problems

Authors: Pop, Vasile, Furdui, Ovidiu

  • Contains a unique collection of enriching problems for a wide spectrum of readership
  • Discusses all important topics related to the theory of square matrices of order 2
  • Presents an enriching source of material for a wide swath of potential readers 
  • Accessible to readers with a modest background in mathematics
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Buy this book

eBook $44.99
price for USA (gross)
valid through November 5, 2017
  • ISBN 978-3-319-54939-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.99
price for USA
valid through November 5, 2017
  • ISBN 978-3-319-54938-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

This unique and innovative book presents an exciting and complete detail of all the important topics related to the theory of square matrices of order 2. The readers exploring every detailed aspect of matrix theory are gently led toward understanding advanced topics. They will follow every notion of matrix theory with ease, accumulating a thorough understanding of algebraic and geometric aspects of matrices of order 2. The prime jewel of this book is its offering of an unusual collection of problems, theoretically motivated, most of which are new, original, and seeing the light of publication for the first time in the literature. Nearly all of the exercises are presented with detailed solutions and vary in difficulty from easy to more advanced. Many problems are particularly challenging. These, and not only these, invite the reader to unleash their creativity and research capabilities and to discover their own methods of attacking a problem.

Matrices have a vast practical importance to mathematics, science, and engineering; therefore the readership of this book is intended to be broad: high school students wishing to learn the fundamentals of matrix theory, first year students who like to participate in mathematical competitions, graduate students who want to learn more about an application of a certain technique, doctoral students who are preparing for their prelim exams in linear algebra, and linear algebra instructors. Chapters 1–3 complement a standard linear algebra course. Pure and applied mathematicians who use matrix theory for their applications will find this book useful as a refresher. In fact, anyone who is willing to explore the methodologies discussed in this book and work through a collection of problems involving matrices of order 2 will be enriched.

About the authors

Vasile Pop is an associate professor of mathematics at the Technical University of Cluj-Napoca, Romania. He teaches linear algebra and functional equation classes and coaches students for SEEMOUS as well as high school students for the International Mathematical Olympiad.

Ovidiu Furdui is an associate professor of mathematics at the Technical University of Cluj-Napoca, Romania. He has published more than 300 problems in journals, with a problem column, from all over the world and he is the author of the Springer text Limits, Series and Fractional Part Integrals.

Reviews

“This is a book that contains almost everything you would like to know about 2 x 2 matrices. … the book is addressed mainly to advanced high school students, undergraduate and graduate students and professionals according to their needs for results about 2 x 2 matrices.” (Andreas Arvanitoyeorgos, zbMATH 1367.15001, 2017) 


Table of contents (6 chapters)

  • Matrices of order 2

    Pop, Vasile (et al.)

    Pages 1-62

  • The Cayley–Hamilton Theorem

    Pop, Vasile (et al.)

    Pages 63-106

  • Applications of Cayley–Hamilton Theorem

    Pop, Vasile (et al.)

    Pages 107-182

  • Functions of matrices. Matrix calculus

    Pop, Vasile (et al.)

    Pages 183-280

  • Applications of matrices to plane geometry

    Pop, Vasile (et al.)

    Pages 281-313

Buy this book

eBook $44.99
price for USA (gross)
valid through November 5, 2017
  • ISBN 978-3-319-54939-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.99
price for USA
valid through November 5, 2017
  • ISBN 978-3-319-54938-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Square Matrices of Order 2
Book Subtitle
Theory, Applications, and Problems
Authors
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-54939-2
DOI
10.1007/978-3-319-54939-2
Hardcover ISBN
978-3-319-54938-5
Edition Number
1
Number of Pages
XXII, 370
Number of Illustrations and Tables
1 b/w illustrations, 7 illustrations in colour
Topics