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Cover: 9780792336143 | Foundations of Linear Algebra | Jonathan S. Golan | Buch | viii | 1995
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Foundations of Linear Algebra
Buch von Jonathan S. Golan
Sprache: Englisch

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Beschreibung
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.
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.
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 1995
Fachbereich: Arithmetik & Algebra
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Texts in the Mathematical Sciences
Inhalt: viii
237 S.
ISBN-13: 9780792336143
ISBN-10: 0792336143
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Golan, Jonathan S.
Hersteller: Springer Netherland
Springer Netherlands
Texts in the Mathematical Sciences
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 241 x 160 x 19 mm
Von/Mit: Jonathan S. Golan
Erscheinungsdatum: 31.08.1995
Gewicht: 0,541 kg
Artikel-ID: 101948459
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 1995
Fachbereich: Arithmetik & Algebra
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Texts in the Mathematical Sciences
Inhalt: viii
237 S.
ISBN-13: 9780792336143
ISBN-10: 0792336143
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Golan, Jonathan S.
Hersteller: Springer Netherland
Springer Netherlands
Texts in the Mathematical Sciences
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 241 x 160 x 19 mm
Von/Mit: Jonathan S. Golan
Erscheinungsdatum: 31.08.1995
Gewicht: 0,541 kg
Artikel-ID: 101948459
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