Verfügbarkeit: Linear algebra

Linear algebra:

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Bibliographische Detailangaben
1. Verfasser:	Lang, Serge 1927-2005 (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	New York u.a. Springer 1989
Ausgabe:	3. ed., 2. corr. printing
Schriftenreihe:	Undergraduate texts in mathematics Springer books on elementary mathematics.
Schlagworte:	Algèbres linéaires Algebras, Linear Lineare Algebra Numerisches Verfahren ALGOL Numerische Mathematik Eigenwertproblem Matrizengleichung Einführung Aufsatzsammlung Lehrbuch
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	IX, 285 S. graph. Darst.
ISBN:	0387964126 3540964126

Internformat

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Datensatz im Suchindex

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adam_text	IMAGE 1 SERGE LANG LINEAR ALGEBRA THIRD EDITION WITH 21 ILLUSTRATIONS SPRINGER 2008 AGI-INFORMATION MANAGEMENT CONSULTANTS MAY BE USED FOR PERSONAL PURPORSES ONLY OR BY LIBRARIES ASSOCIATED TO DANDELON.COM NETWORK. IMAGE 2 CONTENTS CHAPTER I VECTOR SPACES 1 §1. DEFINITIONS , 2§2. BASES 10§3. DIMENSION OF A VECTOR SPACE 15§4. SUMS AND DIRECT SUMS 19 CHAPTER II MATRICES 23 §1. THE SPACE OF MATRICES 23§2. LINEAR EQUATIONS 29§3. MULTIPLICATION OF MATRICES 31 CHAPTER III LINEAR MAPPINGS 43 §1. MAPPINGS 43§2. LINEAR MAPPINGS 51§3. THE KERNEL AND IMAGE OF A LINEAR MAP 59§4. COMPOSITION AND INVERSE OF LINEAR MAPPINGS 66§5. GEOMETRIC APPLICATIONS 72 CHAPTER IV LINEAR MAPS AND MATRICES 81 §1. THE LINEAR MAP ASSOCIATED WITH A MATRIX 81§2. THE MATRIX ASSOCIATED WITH A LINEAR MAP 82§3. BASES, MATRICES, AND LINEAR MAPS 87 IMAGE 3 VIII CONTENTS CHAPTER V SCALAR PRODUCTS AND ORTHOGONALITY 95 §1. SCALAR PRODUCTS 95 §2. ORTHOGONAL BASES, POSITIVE DEFINITE CASE 103 §3. APPLICATION TO LINEAR EQUATIONS; THE RANK 113 §4. BILINEAR MAPS AND MATRICES 118 §5. GENERAL ORTHOGONAL BASES 123 §6. THE DUAL SPACE AND SCALAR PRODUCTS 125 §7. QUADRATIC FORMS 132 §8. SYLVESTER S THEOREM 135 CHAPTER VI DETERMINANTS 140 §1. DETERMINANTS OF ORDER 2 140 §2. EXISTENCE OF DETERMINANTS 143 §3. ADDITIONAL PROPERTIES OF DETERMINANTS 150 §4. CRAMER S RULE . 157 §5. TRIANGULATION OF A MATRIX BY COLUMN OPERATIONS 161 §6. PERMUTATIONS 163 §7. EXPANSION FORMULA AND UNIQUENESS OF DETERMINANTS 168 §8. INVERSE OF A MATRIX 174 §9. THE RANK OF A MATRIX AND SUBDETERMINANTS 177 CHAPTER VII SYMMETRIC, HERMITIAN, AND UNITARY OPERATORS 180 §1. SYMMETRIC OPERATORS 180 §2. HERMITIAN OPERATORS 184 §3. UNITARY OPERATORS 188 CHAPTER VIII EIGENVECTORS AND EIGENVALUES 194 §1. EIGENVECTORS AND EIGENVALUES 194 §2. THE CHARACTERISTIC POLYNOMIAL 200 §3. EIGENVALUES AND EIGENVECTORS OF SYMMETRIC MATRICES 213 §4. DIAGONALIZATION OF A SYMMETRIC LINEAR MAP 218 §5. THE HERMITIAN CASE 225 §6. UNITARY OPERATORS 227 CHAPTER IX POLYNOMIALS AND MATRICES 231 §1. POLYNOMIALS 231 §2. POLYNOMIALS OF MATRICES AND LINEAR MAPS 233 IMAGE 4 CONTENTS IX CHAPTER X TRIANGULATION OF MATRICES AND LINEAR MAPS 237 §1. EXISTENCE OF TRIANGULATION 237 §2. THEOREM OF HAMILTON-CAYLEY 240 §3. DIAGONALIZATION OF UNITARY MAPS 242 CHAPTER XI POLYNOMIALS AND PRIMARY DECOMPOSITION 245 §1. THE EUCLIDEAN ALGORITHM 245 §2. GREATEST COMMON DIVISOR 248 §3. UNIQUE FACTORIZATION 251 §4. APPLICATION TO THE DECOMPOSITION OF A VECTOR SPACE 255 §5. SCHUR S LEMMA 260 §6. THE JORDAN NORMAL FORM 262 CHAPTER XII CONVEX SETS 268 §1. DEFINITIONS 268 §2. SEPARATING HYPERPLANES 270 §3. EXTREME POINTS AND SUPPORTING HYPERPLANES 272 §4. THE KREIN-MILMAN THEOREM 274 APPENDIX I COMPLEX NUMBERS 277 APPENDIX II IWASAWA DECOMPOSITION AND OTHERS 283 INDEX 293
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spellingShingle	Lang, Serge 1927-2005 Linear algebra Algèbres linéaires ram Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd Numerisches Verfahren (DE-588)4128130-5 gnd ALGOL (DE-588)4001182-3 gnd Numerische Mathematik (DE-588)4042805-9 gnd Eigenwertproblem (DE-588)4013802-1 gnd Matrizengleichung (DE-588)4169125-8 gnd
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title	Linear algebra
title_auth	Linear algebra
title_exact_search	Linear algebra
title_full	Linear algebra Serge Lang
title_fullStr	Linear algebra Serge Lang
title_full_unstemmed	Linear algebra Serge Lang
title_short	Linear algebra
title_sort	linear algebra
topic	Algèbres linéaires ram Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd Numerisches Verfahren (DE-588)4128130-5 gnd ALGOL (DE-588)4001182-3 gnd Numerische Mathematik (DE-588)4042805-9 gnd Eigenwertproblem (DE-588)4013802-1 gnd Matrizengleichung (DE-588)4169125-8 gnd
topic_facet	Algèbres linéaires Algebras, Linear Lineare Algebra Numerisches Verfahren ALGOL Numerische Mathematik Eigenwertproblem Matrizengleichung Einführung Aufsatzsammlung Lehrbuch
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001242375&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT langserge linearalgebra

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