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 European University Institute.This item is available to borrow from 1 library branch.
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 European University Institute.
This item is available to borrow from 1 library branch.
 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
 1 online resource (XV, 410 pages)
 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
 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.
 Assigning source
 Provided by publisher
 http://library.link/vocab/creatorName
 Carrell, James B
 Image bit depth
 0
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement
 Springer eBooks
 http://library.link/vocab/subjectName

 Mathematics
 Algebraic geometry
 Commutative algebra
 Commutative rings
 Group theory
 Matrix theory
 Algebra
 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
 Control code
 9780387794280
 Dimensions
 unknown
 Extent
 1 online resource (XV, 410 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9780387794280
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9780387794280
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1003284000
 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
 Control code
 9780387794280
 Dimensions
 unknown
 Extent
 1 online resource (XV, 410 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9780387794280
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9780387794280
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1003284000
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/Groupsmatricesandvectorspacesagroup/W8SOY5IarMM/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/Groupsmatricesandvectorspacesagroup/W8SOY5IarMM/">Groups, matrices, and vector spaces : a group theoretic approach to linear algebra, by James B. Carrell, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>