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Foundations of Linear Algebra / Edition 1

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Overview

This book is an extensively revised version of my textbook "¥esodot HaAlgebra HaLiniarit" (The Foundations of Linear Algebra) used at many universities in Israel. It is designed for a comprehensive one-year course in linear algebra (112 lecture hours) for mathematics majors. Therefore, I assume that the student already has a certain amount of mathematical background - including set theory, mathematical induction, basic analytic geometry, and elementary calculus - as wellas a modicum of mathematical sophistication. My intention is to provide not only a solid basis in the abstract theory of linear algebra, but also to provide examples of the application of this theory to other branches ofmathematics and computer science. Thus, for example, the introduction of finite fields is dictated by the needs of students studying algebraic coding theory as an immediate followup to their linear algebra studies. Many of the students studying linear algebra either are familiar with the care and feeding of computers before they begin their studies or are simultaneously en­ rolled in an introductory computer science course. Therefore, consideration of the more computational aspects of linear algebra - such as the solution of systems of linear equations and the calculation of eigenvalues - is delayed until all students are assumed able to write computer programs for this purpose. Beginning with Chap­ ter VII, there is an implicit assumption that the student has access to a personal computer and knows how to use it.

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Editorial Reviews

Booknews
A text for a one-year undergraduate course for mathematics students who have already studied set theory, mathematical induction, basic analytic geometry, and elementary calculus. Specifically designed to prepare students for advanced work in algebra, differential equations, and functional analysis, by using a transformation rather than matrix perspective and considering arbitrary vector spaces rather than merely finite- dimensional ones. Translated from Yesodot HaAlgebra HaLinearit, published by Dekel, Tel Aviv, in 1992. No bibliography. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9789048145928
  • Publisher: Springer Netherlands
  • Publication date: 12/9/2010
  • Series: Texts in the Mathematical Sciences (closed) Series , #11
  • Edition description: Softcover reprint of hardcover 1st ed. 1995
  • Edition number: 1
  • Pages: 237
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.52 (d)

Table of Contents

Preface. Basic notation and terminology. I. Fields and integral domains. II. Vector spaces. III. Linear independence and dimension. IV. Linear transformations. V. Endomorphism rings of vector spaces. VI. Representation of linear transformations by matrices. VII. Rings of square matrices. VIII. Systems of linear equations. IX. Determinants. X. Eigenvectors and eigenvalues. XI. The Jordan canonical form. XII. The dual space. XIII. Inner product spaces. XIV. Endomorphisms of inner product spaces. XV. The Moore-Penrose pseudoinverse. XVI. Bilinear transformations and forms. XVII. Algebras over a field. Index.

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