A Guide to Advanced Linear Algebra. (Record no. 79825)
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| fixed length control field | 05163nam a22004453i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC3330370 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240729125049.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2011 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780883859674 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780883853511 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC3330370 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL3330370 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (CaPaEBR)ebr10728519 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)929120459 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA184.2 -- .W45 2011eb |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 516.3/55 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Weintraub, Steven H. |
| 245 12 - TITLE STATEMENT | |
| Title | A Guide to Advanced Linear Algebra. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2011. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2011. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (266 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | front cover -- copyright page -- title page -- Preface -- Contents -- 1 Vector spaces and linear transformations -- 1.1 Basic definitions and examples -- 1.2 Basis and dimension -- 1.3 Dimension counting and applications -- 1.4 Subspaces and direct sum decompositions -- 1.5 Affine subspaces and quotient spaces -- 1.6 Dual spaces -- 2 Coordinates -- 2.1 Coordinates for vectors -- 2.2 Matrices for linear transformations -- 2.3 Change of basis -- 2.4 The matrix of the dual -- 3 Determinants -- 3.1 The geometry of volumes -- 3.2 Existence and uniqueness of determinants -- 3.3 Further properties -- 3.4 Integrality -- 3.5 Orientation -- 3.6 Hilbert matrices -- 4 The structure of alinear transformation I -- 4.1 Eigenvalues, eigenvectors, and generalized eigenvectors -- 4.2 Some structural results -- 4.3 Diagonalizability -- 4.4 An application todifferential equations -- 5 The structure of a linear transformation II -- 5.1 Annihilating, minimum, and characteristic polynomials -- 5.2 Invariant subspaces and quotient spaces -- 5.3 The relationship between the characteristic and minimum polynomials -- 5.4 Invariant subspaces and invariant complements -- 5.5 Rational canonical form -- 5.6 Jordan canonical form -- 5.7 An algorithm for Jordan canonical form and Jordan basis -- 5.8 Field extensions -- 5.9 More than one linear transformation -- 6 Bilinear, sesquilinear,and quadratic forms -- 6.1 Basic definitions and results -- 6.2 Characterization and classification theorems -- 6.3 The adjoint of a linear transformation -- 7 Real and complex inner product spaces -- 7.1 Basic definitions -- 7.2 The Gram-Schmidt process -- 7.3 Adjoints, normal linear transformations, and the spectral theorem -- 7.4 Examples -- 7.5 The singular value decomposition -- 8 Matrix groups as Lie groups -- 8.1 Definition and first examples -- 8.2 Isometry groups of forms. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Appendix A: Polynomials -- A.1 Basic properties -- A.2 Unique factorization -- A.3 Polynomials as expressions and polynomials as functions -- Appendix B: Modules over principal ideal domains -- B.1 Definitions and structure theorems -- B.2 Derivation of canonical forms -- Bibliography -- Index -- About the Author. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | Linear algebra occupies a central place in modern mathematics. This book provides a rigorous and thorough development of linear algebra at an advanced level, and is directed at graduate students and professional mathematicians. It approaches linear algebra from an algebraic point of view, but its selection of topics is governed not only for their importance in linear algebra itself, but also for their applications throughout mathematics. Students in algebra, analysis, and topology will find much of interest and use to them, and the careful treatment and breadth of subject matter will make this book a valuable reference for mathematicians throughout their professional lives.Topics treated in this book include: vector spaces and linear transformations; dimension counting and applications; representation of linear transformations by matrices; duality; determinants and their uses; rational and especially Jordan canonical form; bilinear forms; inner product spaces; normal linear transformations and the spectral theorem; and an introduction to matrix groups as Lie groups.The book treats vector spaces in full generality, though it concentrates on the finite dimensional case. Also, it treats vector spaces over arbitrary fields, specializing to algebraically closed fields or to the fields of real and complex numbers as necessary. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Algebras, Linear. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Weintraub, Steven H. |
| Title | A Guide to Advanced Linear Algebra |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2011 |
| International Standard Book Number | 9780883853511 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3330370">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3330370</a> |
| Public note | Click to View |
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