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Groups, matrices, and vector spaces [electronic resource] : a group theoretic approach to linear algebra

Groups, matrices, and vector spaces [electronic resource] : a group theoretic approach to linear algebra

Material type
E-Book(소장)
Personal Author
Carrell, James B.
Title Statement
Groups, matrices, and vector spaces [electronic resource] : a group theoretic approach to linear algebra / James B. Carrell.
Publication, Distribution, etc
New York :   Springer,   c2017.  
Physical Medium
1 online resource (xvii, 410 p.).
ISBN
9780387794280
요약
This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory and cryptography are interwoven throughout. Each section ends with ample practice problems assisting the reader to better understand the material. Some of the applications are illustrated in the chapter appendices. The author's unique melding of topics evolved from a two semester course that he taught at the University of British Columbia consisting of an undergraduate honors course on abstract linear algebra and a similar course on the theory of groups. The combined content from both makes this rare text ideal for a year-long course, covering more material than most linear algebra texts. It is also optimal for independent study and as a supplementary text for various professional applications. Advanced undergraduate or graduate students in mathematics, physics, computer science and engineering will find this book both useful and enjoyable.
General Note
Title from e-Book title page.  
Content Notes
1. Preliminaries -- 2. Groups and Fields: The Two Fundamental Notions of Algebra -- 3. Vector Spaces -- 4. Linear Mappings -- 5. Eigentheory -- 6. Unitary Diagonalization and Quadratic Forms -- 7. The Structure Theory of Linear Mappings -- 8. Theorems on Group Theory -- 9. Linear Algebraic Groups: An Introduction -- Bibliography -- Index.
Bibliography, Etc. Note
Includes bibliographical references (p. 403-405) and index.
이용가능한 다른형태자료
Issued also as a book.  
Subject Added Entry-Topical Term
Group theory --Textbooks. Matrices --Textbooks. Vector spaces --Textbooks.
Short cut
URL
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006 m d
007 cr
008 190624s2017 nyu ob 01 0 eng d
020 ▼a 9780387794280
040 ▼a 211009 ▼c 211009 ▼d 211009
050 4 ▼a QA174.2
082 0 4 ▼a 512.2 ▼2 23
084 ▼a 512.2 ▼2 DDCK
090 ▼a 512.2
100 1 ▼a Carrell, James B.
245 1 0 ▼a Groups, matrices, and vector spaces ▼h [electronic resource] : ▼b a group theoretic approach to linear algebra / ▼c James B. Carrell.
260 ▼a New York : ▼b Springer, ▼c c2017.
300 ▼a 1 online resource (xvii, 410 p.).
500 ▼a Title from e-Book title page.
504 ▼a Includes bibliographical references (p. 403-405) and index.
505 0 ▼a 1. Preliminaries -- 2. Groups and Fields: The Two Fundamental Notions of Algebra -- 3. Vector Spaces -- 4. Linear Mappings -- 5. Eigentheory -- 6. Unitary Diagonalization and Quadratic Forms -- 7. The Structure Theory of Linear Mappings -- 8. Theorems on Group Theory -- 9. Linear Algebraic Groups: An Introduction -- Bibliography -- Index.
520 ▼a This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory and cryptography are interwoven throughout. Each section ends with ample practice problems assisting the reader to better understand the material. Some of the applications are illustrated in the chapter appendices. The author's unique melding of topics evolved from a two semester course that he taught at the University of British Columbia consisting of an undergraduate honors course on abstract linear algebra and a similar course on the theory of groups. The combined content from both makes this rare text ideal for a year-long course, covering more material than most linear algebra texts. It is also optimal for independent study and as a supplementary text for various professional applications. Advanced undergraduate or graduate students in mathematics, physics, computer science and engineering will find this book both useful and enjoyable.
530 ▼a Issued also as a book.
538 ▼a Mode of access: World Wide Web.
650 0 ▼a Group theory ▼v Textbooks.
650 0 ▼a Matrices ▼v Textbooks.
650 0 ▼a Vector spaces ▼v Textbooks.
856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=https://doi.org/10.1007/978-0-387-79428-0
945 ▼a KLPA
991 ▼a E-Book(소장)

Holdings Information

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No. 1 Location Main Library/e-Book Collection/ Call Number CR 512.2 Accession No. E14013719 Availability Loan can not(reference room) Due Date Make a Reservation Service M

Contents information

Table of Contents

1. Preliminaries -- 2. Groups and Fields: The Two Fundamental Notions of Algebra -- 3. Vector Spaces -- 4. Linear Mappings -- 5. Eigentheory -- 6. Unitary Diagonalization and Quadratic Forms -- 7. The Structure Theory of Linear Mappings -- 8. Theorems on Group Theory -- 9. Linear Algebraic Groups: An Introduction -- Bibliography -- Index.

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