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Denis Serre, "Matrices: Theory and Applications"

In this book, Denis Serre begins by providing a clean and concise introduction to the basic theory of matrices. He then goes on to give many interesting applications of matrices to different aspects of mathematics and also other areas of science and engineering. The book mixes together algebra, analysis, complexity theory and numerical analysis. As such, this book will provide many scientists, not just mathematicians, with a useful and reliable reference. It is intended for advanced undergraduate and graduate students with either applied or theoretical goals. This book is based on a course given by the author at the Ecole Normale Supérieure de Lyon. Denis Serre is Professor of Mathematics at Ecole Normale Supérieure de Lyon and a former member of the Institut Universaire de France. He is a member of numerous editorial boards and the author of Systems of Conservation Laws (Cambridge University Press 2000). The present book is a translation of the original French edition, Les Matrices: Théorie et Pratique, published by Dunod (2001).

Reviews

"This is a first-year graduate text that will be of considerable value to students with any of a wide variety of potential research objectives. Both the proofs and the general explanations are unusually detailed…There are 165 well-designed exercises, many of which provide additional information on topics treated in the text." (Mathematical Reviews)

"The main motivation of the author is to … obtain a textbook that is suitable for a wide range of applications and hence for the different audiences deeply interested in matrices. The main goal is certainly achieved. … The complex theoretical language, the presentation of modern numerical techniques and the classical algebraic basics make this textbook an excellent source for graduate students in each field using matrices. It can be recommended both for use in the classroom and for independent study." (Péter Hajnal, Acta Scientiarum Mathematicarum, 71, 2005)

"This is a first-year graduate text that will be of considerable value to students with any of a wide variety of potential research objectives. Both the proofs and the general explanations are unusually complete and detailed … . There are 165 well-designed exercises, many of which provide additional information on topics treated in the text. Full solutions are available on the author’s website." (R.J. Bumcrot, Mathematical Reviews, 2003 h)

"Denis Serre provides a clear and concise introduction to the basic theory of matrices. … The book combines algebra, analysis, complexity theory, and numerical analysis, and it will provide many scientists, not just mathematicians, with a useful and reliable reference. … The book is intended for advanced undergraduate and graduate students with either applied or theoretical goals." (L’enseignement mathématique, 48:3-4), 2002)

"Serre … offers another volume in this series of mathematics work; it is designed for graduate students or upper-level undergraduates who wish to study matrix theory or need a reference in that subject. The discussion is approached from a strongly algebraic viewpoint and is quite concise and thorough. … There are about 170 exercises spread throughout, all theoretical in nature. Extensive bibliography. A useful resource for anyone who uses matrix theory in his or her work. Summing Up: Highly recommended." (J.H. Ellison, Choice, April 2003)

"This text offers an advanced course in matrix theory aimed at a student with a good background in analysis, providing a selection of advanced topics in matrices over the real or complex fields without attempting to be encyclopedic. … The book contains a large number of exercises, many interesting and challenging, including extensions of results discussed in the main text and alternative proofs of some theorems." (J.D. Dixon, Zentralblatt MATH, 1011, 2003)

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