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The Resource Groups, Matrices, and Vector Spaces : A Group Theoretic Approach to Linear Algebra, by James B. Carrell, (electronic resource)
Groups, Matrices, and Vector Spaces : A Group Theoretic Approach to Linear Algebra, by James B. Carrell, (electronic resource)
Resource Information
The item Groups, Matrices, and Vector Spaces : A Group Theoretic Approach to Linear Algebra, by James B. Carrell, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Groups, Matrices, and Vector Spaces : A Group Theoretic Approach to Linear Algebra, by James B. Carrell, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 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 yearlong 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
 Language
 eng
 Extent
 XV, 410 p.
 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
 Isbn
 9780387794280
 Label
 Groups, Matrices, and Vector Spaces : A Group Theoretic Approach to Linear Algebra
 Title
 Groups, Matrices, and Vector Spaces
 Title remainder
 A Group Theoretic Approach to Linear Algebra
 Statement of responsibility
 by James B. Carrell
 Subject

 Algebra
 Group Theory and Generalizations
 Algebraic Geometry
 Commutative algebra
 Geometry, Algebraic
 Commutative Rings and Algebras
 Group theory
 Geometry, Algebraic
 Electronic resources
 Mathematics
 Commutative algebra
 Linear and Multilinear Algebras, Matrix Theory
 Mathematics
 Commutative rings
 Algebra
 Commutative rings
 Group theory
 Matrix theory
 Language
 eng
 Summary
 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 yearlong 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
 http://library.link/vocab/creatorName
 Carrell, James B
 Image bit depth
 0
 LC call number
 QA251.3
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName
 SpringerLink
 http://library.link/vocab/subjectName

 Mathematics
 Geometry, Algebraic
 Commutative algebra
 Commutative rings
 Group theory
 Matrix theory
 Algebra
 Mathematics
 Commutative Rings and Algebras
 Linear and Multilinear Algebras, Matrix Theory
 Group Theory and Generalizations
 Algebraic Geometry
 Label
 Groups, Matrices, and Vector Spaces : A Group Theoretic Approach to Linear Algebra, by James B. Carrell, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 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
 Dimensions
 unknown
 Extent
 XV, 410 p.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9780387794280
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9780387794280
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9780387794280
 Label
 Groups, Matrices, and Vector Spaces : A Group Theoretic Approach to Linear Algebra, by James B. Carrell, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 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
 Dimensions
 unknown
 Extent
 XV, 410 p.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9780387794280
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9780387794280
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9780387794280
Subject
 Algebra
 Algebra
 Algebraic Geometry
 Commutative Rings and Algebras
 Commutative algebra
 Commutative algebra
 Commutative rings
 Commutative rings
 Electronic resources
 Geometry, Algebraic
 Geometry, Algebraic
 Group Theory and Generalizations
 Group theory
 Group theory
 Linear and Multilinear Algebras, Matrix Theory
 Mathematics
 Mathematics
 Matrix theory
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