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 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.--
- 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 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.--
- 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
- 978-0-387-79428-0
- 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, non-commercial 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
- 10.1007/978-0-387-79428-0
- 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
- 978-0-387-79428-0
- 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, non-commercial 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
- 10.1007/978-0-387-79428-0
- 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 fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.eui.eu/portal/Groups-matrices-and-vector-spaces--a-group/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/Groups-matrices-and-vector-spaces--a-group/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>