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A first course in linear algebra / Minking Eie, Shou-Te Chang
New Jersey : World Scientific, 2016
xii, 376 pages. : illustrations ; 24 cm.
Ký hiệu phân loại (DDC): 512.5
A First Course in Linear Algebra is written by two experts from algebra who have more than 20 years of experience in algebra, linear algebra and number theory. It prepares students with no background in Linear Algebra. Students, after mastering the materials in this textbook, can already understand any Linear Algebra used in more advanced books and research papers in Mathematics or in other scientific disciplines.This book provides a solid foundation for the theory dealing with finite dimensional vector spaces. It explains in details the relation between linear transformations and matrices. One may thus use different viewpoints to manipulate a matrix instead of a one-sided approach. Although most of the examples are for real and complex matrices, a vector space over a general field is briefly discussed. Several optional sections are devoted to applications to demonstrate the power of Linear Algebra
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2
Lectures on groups and vector spaces for physicists / C. J. Isham
Singapore : World Scientific, 1989
vii, 219 pages. : illustrations ; 23 cm. ; 23 cm.
Ký hiệu phân loại (DDC): 530.15
These notes are the contents of a lecture course given to third year physics undergraduates at the Imperial College who are taking the theoretical physics option. The subject of "Algebra and Groups" is of considerable importance in a number of branches of modern theoretical physics, and therefore one major objective of the course is to introduce the students to the basic ideas on the subject, bearing in mind the potential applications to quantum theory. However, another equally important aim of the course is to introduce the student to the art of genuine "mathematical" thinking. The notes are therefore written in a more precise mathematical style than is usually the case in courses aimed at physics students. Quite apart from the general educational value of such an exposure to abstract thinking, it is also the case that much modern theoretical physics draws on sophisticated ideas from pure mathematics and therefore it is most important that a perspective graduate student can approach these subjects without experiencing a total culture shock! The course is divided into three parts. The first is a short introduction to general group theory, with particular emphasis being placed on the matrix Lie groups that play such a crucial role in modern theoretical physics. The second part deals with the theory of vector spaces, with particular attention being paid to the theory of Hilbert spaces and the basic analytical techniques that are needed to handle the infinite dimensional situation. The final part of the course is a short introduction to the theory of group representations and the associated theory of characters.
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Linear algebra : pure & applied / Edgar G. Goodaire
[Hoboken], New Jersey, : World Scientific, 2014
xvi, 716 pages. : illustrations ; 24 cm.
Ký hiệu phân loại (DDC): 512.5
This is a matrix-oriented approach to linear algebra that covers the traditional material of the courses generally known as “Linear Algebra I” and “Linear Algebra II” throughout North America, but it also includes more advanced topics such as the pseudoinverse and the singular value decomposition that make it appropriate for a more advanced course as well. As is becoming increasingly the norm, the book begins with the geometry of Euclidean 3-space so that important concepts like linear combination, linear independence and span can be introduced early and in a “real” context. The book reflects the author's background as a pure mathematician — all the major definitions and theorems of basic linear algebra are covered rigorously — but the restriction of vector spaces to Euclidean n-space and linear transformations to matrices, for the most part, and the continual emphasis on the system Ax=b, make the book less abstract and more attractive to the students of today than some others. As the subtitle suggests, however, applications play an important role too. Coding theory and least squares are recurring themes. Other applications include electric circuits, Markov chains, quadratic forms and conic sections, facial recognition and computer graphics.
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Selected papers of J.L. Koszul / J.L. Koszul (editor)
Singapore : World Scientific, 1994
viii, 285 pages. ; 26 cm.
Ký hiệu phân loại (DDC): 512.54
Organized in chronological order, this volume brings together the major contributions of J. L. Koszul and some expository articles
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