A Guide to Advanced Linear Algebra /:
"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 importan...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2012.
|
| Schriftenreihe: | Dolciani mathematical expositions.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "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"-- |
| Beschreibung: | Title from publishers bibliographic system (viewed on 30 Jan 2012). |
| Beschreibung: | 1 online resource |
| ISBN: | 9780883859674 088385967X |
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| 505 | 0 | |a 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 | |
| 505 | 8 | |a 3.2 Existence and uniqueness of determinants3.3 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 | |
| 505 | 8 | |a 5.3 The relationship between the characteristic and minimum polynomials5.4 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 | |
| 505 | 8 | |a 7.2 The Gram-Schmidt process7.3 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 -- 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 | |
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| contents | 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 determinants3.3 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 polynomials5.4 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 process7.3 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 -- 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 |
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| spelling | Weintraub, Steven H. A Guide to Advanced Linear Algebra / Steven H. Weintraub. Cambridge : Cambridge University Press, 2012. 1 online resource text txt rdacontent computer c rdamedia online resource cr rdacarrier Dolciani Mathematical Expositions ; v. 44 Title from publishers bibliographic system (viewed on 30 Jan 2012). 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 determinants3.3 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 polynomials5.4 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 process7.3 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 -- 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 "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"-- Source other than Library of Congress. Algebras, Linear. http://id.loc.gov/authorities/subjects/sh85003441 Algèbre linéaire. MATHEMATICS Geometry Algebraic. bisacsh MATHEMATICS Algebra Linear. bisacsh Algebras, Linear fast Print version: Weintraub, Steven H. Guide to Advanced Linear Algebra. Washington : Mathematical Association of America, ©2014 9780883853511 Dolciani mathematical expositions. http://id.loc.gov/authorities/names/n42009859 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=450279 Volltext |
| spellingShingle | Weintraub, Steven H. A Guide to Advanced Linear Algebra / Dolciani mathematical expositions. 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 determinants3.3 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 polynomials5.4 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 process7.3 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 -- 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 Algebras, Linear. http://id.loc.gov/authorities/subjects/sh85003441 Algèbre linéaire. MATHEMATICS Geometry Algebraic. bisacsh MATHEMATICS Algebra Linear. bisacsh Algebras, Linear fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85003441 |
| title | A Guide to Advanced Linear Algebra / |
| title_auth | A Guide to Advanced Linear Algebra / |
| title_exact_search | A Guide to Advanced Linear Algebra / |
| title_full | A Guide to Advanced Linear Algebra / Steven H. Weintraub. |
| title_fullStr | A Guide to Advanced Linear Algebra / Steven H. Weintraub. |
| title_full_unstemmed | A Guide to Advanced Linear Algebra / Steven H. Weintraub. |
| title_short | A Guide to Advanced Linear Algebra / |
| title_sort | guide to advanced linear algebra |
| topic | Algebras, Linear. http://id.loc.gov/authorities/subjects/sh85003441 Algèbre linéaire. MATHEMATICS Geometry Algebraic. bisacsh MATHEMATICS Algebra Linear. bisacsh Algebras, Linear fast |
| topic_facet | Algebras, Linear. Algèbre linéaire. MATHEMATICS Geometry Algebraic. MATHEMATICS Algebra Linear. Algebras, Linear |
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