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Foundations of Linear Algebra : Texts in the Mathematical Sciences - Jonathan S. Golan

Foundations of Linear Algebra

Texts in the Mathematical Sciences

Hardcover Published: 31st August 1995
ISBN: 9780792336143
Number Of Pages: 237

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This book is an extensively revised version of my textbook "Yesodot 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.

Basic Notation and Terminologyp. 1
Fields and Integral Domainsp. 3
Vector Spacesp. 12
Linear Independence and Dimensionp. 24
Linear Transformationsp. 41
Endomorphism Rings of Vector Spacesp. 55
Representation of Linear Transformations by Matricesp. 65
Rings of Square Matricesp. 76
Systems of Linear Equationsp. 93
Determinantsp. 111
Eigenvectors and Eigenvaluesp. 127
The Jordan Canonical Formp. 144
The Dual Spacep. 154
Inner Product Spacesp. 161
Endomorphisms of Inner Product Spacesp. 183
The Moore-Penrose Pseudoinversep. 198
Bilinear transformations and formsp. 204
Algebras over a fieldp. 219
Indexp. 228
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792336143
ISBN-10: 0792336143
Series: Texts in the Mathematical Sciences
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 237
Published: 31st August 1995
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6  x 1.6
Weight (kg): 0.53

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