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Square Matrices of Order 2

Theory, Applications, and Problems

  • Textbook
  • © 2017

Overview

Authors:
  1. Vasile Pop

    1. Department of Mathematics, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

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    You can also search for this author in PubMed   Google Scholar

  2. Ovidiu Furdui

    1. Department of Mathematics, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • 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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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xxii
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  2. Matrices of order 2

    • Vasile Pop, Ovidiu Furdui
    Pages 1-62

  3. The Cayley–Hamilton Theorem

    • Vasile Pop, Ovidiu Furdui
    Pages 63-106

  4. Applications of Cayley–Hamilton Theorem

    • Vasile Pop, Ovidiu Furdui
    Pages 107-182

  5. Functions of matrices. Matrix calculus

    • Vasile Pop, Ovidiu Furdui
    Pages 183-280

  6. Applications of matrices to plane geometry

    • Vasile Pop, Ovidiu Furdui
    Pages 281-313

  7. Conics

    • Vasile Pop, Ovidiu Furdui
    Pages 315-345

  8. Back Matter

    Pages 347-370
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Keywords

About this book

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.

Reviews

“The book is written in a clear and precise style. The book contains a vast collection of problems varying from easy to difficult levels and their detailed solutions, which help the reader to learn some basic and advanced linear algebra. … The book will be interesting for people who like matrix theory and its challenging problems; in particular, for students who are preparing themselves for mathematical competitions.” (Mohammad Sal Moslehian, Mathematical Reviews, September, 2017)



“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) 

Authors and Affiliations

  • Department of Mathematics, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

    Vasile Pop, Ovidiu Furdui

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.


Bibliographic Information

  • Book Title: Square Matrices of Order 2

  • Book Subtitle: Theory, Applications, and Problems

  • Authors: Vasile Pop, Ovidiu Furdui

  • DOI: https://doi.org/10.1007/978-3-319-54939-2

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG 2017

  • Hardcover ISBN: 978-3-319-54938-5Published: 13 April 2017

  • Softcover ISBN: 978-3-319-85526-4Published: 09 May 2018

  • eBook ISBN: 978-3-319-54939-2Published: 04 April 2017

  • Edition Number: 1

  • Number of Pages: XXII, 370

  • Number of Illustrations: 1 b/w illustrations, 7 illustrations in colour

  • Topics: Linear and Multilinear Algebras, Matrix Theory

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