# Square Matrices of Order 2

## Theory, Applications, and Problems

• Vasile Pop
• Ovidiu Furdui
Textbook

1. Front Matter
Pages i-xxii
2. Vasile Pop, Ovidiu Furdui
Pages 1-62
3. Vasile Pop, Ovidiu Furdui
Pages 63-106
4. Vasile Pop, Ovidiu Furdui
Pages 107-182
5. Vasile Pop, Ovidiu Furdui
Pages 183-280
6. Vasile Pop, Ovidiu Furdui
Pages 281-313
7. Vasile Pop, Ovidiu Furdui
Pages 315-345
8. Back Matter
Pages 347-370

### Introduction

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.

### Keywords

special matrices problems matrix theory elementary transformations Cayley-Hamilton theorem Jordan canonical theorem powers of matrices binomial matrix Pell's Diophantine equation matrix Gamma function affine applications homothetic transformations degenerate conics nondegenerate conics series mirabilis matrix calculus functions of matrices conics homographic sequences characteristic polynomial matrix Riemann zeta function

#### Authors and affiliations

• Vasile Pop
• 1
• Ovidiu Furdui
• 2
1. 1.Department of MathematicsTechnical University of Cluj-NapocaCluj-NapocaRomania
2. 2.Department of MathematicsTechnical University of Cluj-NapocaCluj-NapocaRomania

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