MARC details
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
080402s2005 nyua b 001 0 eng |
| 010 ## - LIBRARY OF CONGRESS CONTROL NUMBER |
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| LC control number |
2005040244 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
0387247661 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780387247663 |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
(Sirsi) u499 |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
EG-CaNU |
| Transcribing agency |
EG-CaNU |
| Modifying agency |
EG-CaNU |
| 042 ## - AUTHENTICATION CODE |
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| Authentication code |
ncode |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
512.5 |
| Edition number |
22 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Roman, Steven. |
| 9 (RLIN) |
4737 |
| 245 10 - TITLE STATEMENT |
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| Title |
Advanced linear algebra / |
| Statement of responsibility, etc. |
Steven Roman. |
| 250 ## - EDITION STATEMENT |
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| Edition statement |
2nd ed. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. |
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| Place of publication, distribution, etc. |
New York : |
| Name of publisher, distributor, etc. |
Springer, |
| Date of publication, distribution, etc. |
c2005. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xvi, 482 p. : |
| Other physical details |
ill. ; |
| Dimensions |
25 cm. |
| 490 0# - SERIES STATEMENT |
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| Series statement |
Graduate texts in mathematics ; |
| Volume/sequential designation |
135 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc. note |
Includes bibliographical references (p. [473]-474) and index. |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Miscellaneous information |
Ch. 0. |
| Title |
Preliminaries -- |
| Miscellaneous information |
Pt. 1. |
| Title |
Preliminaries -- |
| -- |
Matrices -- |
| -- |
Determinants -- |
| -- |
Polynomials. Functions -- |
| -- |
Equivalence Relations -- |
| -- |
Zorn’s Lemma -- |
| -- |
Cardinality -- |
| Miscellaneous information |
Pt. 2. |
| Title |
Algebraic Structures -- |
| -- |
Groups -- |
| -- |
Rings -- |
| -- |
Integral Domains -- |
| -- |
Ideals and Principal Ideal Domains -- |
| -- |
Prime Elements -- |
| -- |
Fields -- |
| -- |
The Characteristic of a Ring -- |
| Miscellaneous information |
Pt. 1. |
| Title |
Basic Linear Algebra -- |
| Miscellaneous information |
Ch. 1. |
| Title |
Vector Spaces -- |
| -- |
Vector Spaces -- |
| -- |
Subspaces -- |
| -- |
The Lattice of Subspaces -- |
| -- |
Direct Sums -- |
| -- |
Spanning Sets and Linear Independence -- |
| -- |
The Dimension of a Vector Space -- |
| -- |
The Row and Column Space of a Matrix -- |
| -- |
Coordinate Matrices -- |
| -- |
Exercises -- |
| Miscellaneous information |
Ch. 2. |
| Title |
Linear Transformations -- |
| -- |
Linear Transformations -- |
| -- |
The Kernel and Image of a Linear Transformation -- |
| -- |
Isomorphisms -- |
| -- |
The Rank Plus Nullity Theorem -- |
| -- |
Linear Transformations from F[superscript n] to F[superscript m] -- |
| -- |
Change of Basis Matrices -- |
| -- |
The Matrix of a Linear Transformation -- |
| -- |
Change of Bases for Linear Transformations -- |
| -- |
Equivalence of Matrices -- |
| -- |
Similarity of Matrices -- |
| -- |
Invariant Subspaces and Reducing Pairs -- |
| -- |
Exercises -- |
| Miscellaneous information |
Ch. 3. |
| Title |
Isomorphism Theorems -- |
| -- |
Quotient Spaces -- |
| -- |
The First Isomorphism Theorem -- |
| -- |
The Dimension of a Quotient Space -- |
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Additional Isomorphism Theorems -- |
| -- |
Linear Functionals -- |
| -- |
Dual Bases -- |
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Reflexivity -- |
| -- |
Annihilators -- |
| -- |
Operator Adjoints -- |
| -- |
Exercises -- |
| Miscellaneous information |
Ch. 4. |
| Title |
Modules I -- |
| -- |
Motivation -- |
| -- |
Modules -- |
| -- |
Submodules -- |
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Direct Sums -- |
| -- |
Spanning Sets -- |
| -- |
Linear Independence -- |
| -- |
Homomorphisms -- |
| -- |
Free Modules -- |
| -- |
Summary -- |
| -- |
Exercises -- |
| Miscellaneous information |
Ch. 5. |
| Title |
Modules II -- |
| -- |
Quotient Modules -- |
| -- |
Quotient Rings and Maximal Ideals -- |
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Noetherian Modules -- |
| -- |
The Hilbert Basis Theorem -- |
| -- |
Exercises -- |
| Miscellaneous information |
Ch. 6. |
| Title |
Modules over Principal Ideal Domains -- |
| -- |
Free Modules over a Principal Ideal Domain -- |
| -- |
Torsion Modules -- |
| -- |
The Primary Decomposition Theorem -- |
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The Cyclic Decomposition Theorem for Primary Modules -- |
| -- |
Uniqueness -- |
| -- |
The Cyclic Decomposition Theorem -- |
| -- |
Exercises -- |
| Miscellaneous information |
Ch. 7. |
| Title |
Structure of a Linear Operator -- |
| -- |
A Brief Review -- |
| -- |
The Module Associated with a Linear Operator -- |
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Submodules and Invariant Subspaces -- |
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Orders and the Minimal Polynomial -- |
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Cyclic Submodules and Cyclic Subspaces -- |
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Summary -- |
| -- |
The Decomposition of V. -- |
| -- |
The Rational Canonical Form -- |
| -- |
Exercises -- |
| Miscellaneous information |
Ch. 8. |
| Title |
Eigenvalues and Eigenvectors -- |
| -- |
The Characteristic Polynomial of an Operator -- |
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Eigenvalues and Eigenvectors -- |
| -- |
The Cayley-Hamilton Theorem -- |
| -- |
The Jordan Canonical Form -- |
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Geometric and Algebraic Multiplicities -- |
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Diagonalizable Operators -- |
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Projections -- |
| -- |
The Algebra of Projections -- |
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Resolutions of the Identity -- |
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Projections and Diagonalizability -- |
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Projections and Invariance -- |
| -- |
Exercises -- |
| Miscellaneous information |
Ch. 9. |
| Title |
Real and Complex Inner Product Spaces -- |
| -- |
Introduction -- |
| -- |
Norm and Distance -- |
| -- |
Isometries -- |
| -- |
Orthogonality -- |
| -- |
Orthogonal and Orthonormal Sets -- |
| -- |
The Projection Theorem -- |
| -- |
The Gram-Schmidt Orthogonalization Process -- |
| -- |
The Riesz Representation Theorem -- |
| -- |
Exercises -- |
| Miscellaneous information |
Ch. 10. |
| Title |
Spectral Theorem for Normal Operators -- |
| -- |
The Adjoint of a Linear Operator -- |
| -- |
Orthogonal Diagonalizability -- |
| -- |
Motivation -- |
| -- |
Self-Adjoint Operators -- |
| -- |
Unitary Operators -- |
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Normal Operators -- |
| -- |
Orthogonal Diagonalization -- |
| -- |
Orthogonal Projections -- |
| -- |
Orthogonal Resolutions of the Identity -- |
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The Spectral Theorem -- |
| -- |
Functional Calculus -- |
| -- |
Positive Operators -- |
| -- |
The Polar Decomposition of an Operator -- |
| -- |
Exercises -- |
| Miscellaneous information |
Pt. 2. |
| Title |
Topics -- |
| Miscellaneous information |
Ch. 11. |
| Title |
Metric Vector Spaces -- |
| -- |
Symmetric, Skew-symmetric and Alternate Forms -- |
| -- |
The Matrix of a Bilinear Form -- |
| -- |
Quadratic Forms -- |
| -- |
Linear Functionals -- |
| -- |
Orthogonality -- |
| -- |
Orthogonal Complements -- |
| -- |
Orthogonal Direct Sums -- |
| -- |
Quotient Spaces -- |
| -- |
Symplectic Geometry - Hyperbolic Planes -- |
| -- |
Orthogonal Geometry - Orthogonal Bases -- |
| -- |
The Structure of an Orthogonal Geometry -- |
| -- |
Isometries -- |
| -- |
Symmetries -- |
| -- |
Witt’s Cancellation Theorem -- |
| -- |
Witt’s Extension Theorem -- |
| -- |
Maximum Hyperbolic Subspaces -- |
| -- |
Exercises -- |
| Miscellaneous information |
Ch. 12. |
| Title |
Metric Spaces -- |
| -- |
The Definition -- |
| -- |
Open and Closed Sets -- |
| -- |
Convergence in a Metric Space -- |
| -- |
The Closure of a Set -- |
| -- |
Dense Subsets -- |
| -- |
Continuity -- |
| -- |
Completeness -- |
| -- |
Isometries -- |
| -- |
The Completion of a Metric Space -- |
| -- |
Exercises -- |
| Miscellaneous information |
Ch. 13. |
| Title |
Hilbert Spaces -- |
| -- |
A Brief Review -- |
| -- |
Hilbert Spaces -- |
| -- |
Infinite Series -- |
| -- |
An Approximation Problem -- |
| -- |
Hilbert Bases -- |
| -- |
Fourier Expansions -- |
| -- |
A Characterization of Hilbert Bases -- |
| -- |
Hilbert Dimension -- |
| -- |
A Characterization of Hilbert Spaces -- |
| -- |
The Riesz Representation Theorem -- |
| -- |
Exercises -- |
| Miscellaneous information |
Ch. 14. |
| Title |
Tensor Products -- |
| -- |
Free Vector Spaces -- |
| -- |
Another Look at the Direct Sum -- |
| -- |
Bilinear Maps and Tensor Products -- |
| -- |
Properties of the Tensor Product -- |
| -- |
The Tensor Product of Linear Transformations -- |
| -- |
Change of Base Field -- |
| -- |
Multilinear Maps and Iterated Tensor Products -- |
| -- |
Alternating Maps and Exterior Products -- |
| -- |
Exercises -- |
| Miscellaneous information |
Ch. 15. |
| Title |
Affine Geometry -- |
| -- |
Affine Geometry -- |
| -- |
Affine Combinations -- |
| -- |
Affine Hulls -- |
| -- |
The Lattice of Flats -- |
| -- |
Affine Independence -- |
| -- |
Affine Transformations -- |
| -- |
Projective Geometry -- |
| -- |
Exercises -- |
| Miscellaneous information |
Ch. 16. |
| Title |
Umbral Calculus -- |
| -- |
Formal Power Series -- |
| -- |
The Umbral Algebra -- |
| -- |
Formal Power Series as Linear Operators -- |
| -- |
Sheffer Sequences -- |
| -- |
Examples of Sheffer Sequences -- |
| -- |
Umbral Operators and Umbral Shifts -- |
| -- |
Continuous Operators on the Umbral Algebra -- |
| -- |
Operator Adjoints -- |
| -- |
Automorphisms of the Umbral Algebra -- |
| -- |
Derivations of the Umbral Algebra -- |
| -- |
Exercises. |
| 596 ## - |
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| -- |
1 |
| 630 00 - SUBJECT ADDED ENTRY--UNIFORM TITLE |
|---|
| Uniform title |
CIT. |
| 9 (RLIN) |
14 |
| 630 00 - SUBJECT ADDED ENTRY--UNIFORM TITLE |
|---|
| Uniform title |
MOT. |
| 9 (RLIN) |
9971 |
| 630 00 - SUBJECT ADDED ENTRY--UNIFORM TITLE |
|---|
| Uniform title |
ITS. |
| 9 (RLIN) |
160 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Algebras, Linear. |
| 9 (RLIN) |
930 |