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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

자료유형
E-Book(소장)
개인저자
Carrell, James B.
서명 / 저자사항
Groups, matrices, and vector spaces [electronic resource] : a group theoretic approach to linear algebra / James B. Carrell.
발행사항
New York :   Springer,   c2017.  
형태사항
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.
일반주기
Title from e-Book title page.  
내용주기
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.
서지주기
Includes bibliographical references (p. 403-405) and index.
이용가능한 다른형태자료
Issued also as a book.  
일반주제명
Group theory --Textbooks. Matrices --Textbooks. Vector spaces --Textbooks.
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URL
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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)

소장정보

No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 중앙도서관/e-Book 컬렉션/ 청구기호 CR 512.2 등록번호 E14013719 도서상태 대출불가(열람가능) 반납예정일 예약 서비스 M

컨텐츠정보

목차

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.

관련분야 신착자료

Aluffi, Paolo (2021)