Square Matrices of Order 2

Theory, Applications, and Problems

Vasile Pop, Ovidiu Furdui (Autoren)

Buch | Hardcover

XXII, 370 Seiten

2017 | 1st ed. 2017
Springer International Publishing (Verlag)
978-3-319-54938-5 (ISBN)

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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.

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.

Notations.- 1. Matrices of order 2.- 2. The Cayley-Hamilton Theorem.- 3. Applications of Cayley-Hamilton Theorem.- 4. Functions of matrices. Matrix calculus.- 5. Applications of matrices to plane geometry.- 6. Conics. - A. Gems of classical analysis and linear algebra.- B. Trigonometric matrix equations.- References.- Index.

"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)

Erscheinungsdatum	27.04.2017
Vorwort	Dennis S. Bernstein
Zusatzinfo	XXII, 370 p. 8 illus., 7 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	748 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Schlagworte	affine applications • binomial matrix • Cayley-Hamilton theorem • Characteristic Polynomial • conics • degenerate conics • elementary transformations • functions of matrices • homographic sequences • homothetic transformations • Jordan canonical theorem • Matrix Calculus • matrix Gamma function • matrix Riemann zeta function • nondegenerate conics • Pell's Diophantine equation • powers of matrices • problems matrix theory • series mirabilis • special matrices
ISBN-10	3-319-54938-3 / 3319549383
ISBN-13	978-3-319-54938-5 / 9783319549385
Zustand	Neuware