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Linear algebra:

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Bibliographic Details
Main Author:	Smith, Larry (Author)
Format:	Book
Language:	German
Published:	New York [u.a.] Springer 1998
Edition:	3. ed.
Series:	Undergraduate texts in mathematics
Subjects:	Eigenwertproblem Matrizengleichung ALGOL Numerische Mathematik Lineare Algebra Numerisches Verfahren Einführung Lehrbuch
Online Access:	Inhaltsverzeichnis
Physical Description:	XII, 452 S. graph. Darst.
ISBN:	0387984550

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MARC


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adam_text	LARRY SMITH LINEAR ALGEBRA THIRD EDITION WITH 23 ILLUSTRATIONS SPRINGER CONTENTS PREFACE. VU 1. VECTORS IN THE PLANE AND IN SPACE 1 1.1 FIRST STEPS 1 1.2 EXERCISES 12 2. VECTOR SPACES 15 2.1 AXIOMS FOR VECTOR SPACES 15 2.2 CARTESIAN (OR EUCLIDEAN) SPACES 18 2.3 SOME RULES FOR VECTOR ALGEBRA 21 2.4 EXERCISES 22 3. EXAMPLES OF VECTOR SPACES 25 3.1 THREE BASIC EXAMPLES 25 3.2 FURTHER EXAMPLES OF VECTOR SPACES 27 3.3 EXERCISES 30 4. SUBSPACES 35 4.1 BASIC PROPERTIES OF VECTOR SUBSPACES 35 4.2 EXAMPLES OF SUBSPACES 41 4.3 EXERCISES 42 5. LINEAR INDEPENDENCE AND DEPENDENCE 47 5.1 BASIC DEFINITIONS AND EXAMPLES 47 5.2 PROPERTIES OF INDEPENDENT AND DEPENDENT SETS 50 5.3 EXERCISES 53 IX X CONTENTS 6. FINITE-DIMENSIONAL VECTOR SPACES AND BASES 57 6.1 FINITE-DIMENSIONAL VECTOR SPACES 57 6.2 PROPERTIES OF BASES 61 6.3 USING BASES 65 6.4 EXERCISES 71 7. THE ELEMENTS OF VECTOR SPACES: A SUMMING UP 75 7.1 NUMERICAL EXAMPLES 75 7.2 EXERCISES 82 8. LINEAR TRANSFORMATIONS 85 8.1 DEFINITION OF LINEAR TRANSFORMATIONS 85 8.2 EXAMPLES OF LINEAR TRANSFORMATIONS 89 8.3 PROPERTIES OF LINEAR TRANSFORMATIONS 91 8.4 IMAGES AND KERNELS OF LINEAR TRANSFORMATIONS 94 8.5 SOME FUNDAMENTAL CONSTRUCTIONS 98 8.6 ISOMORPHISM OF VECTOR SPACES 102 8.7 EXERCISES 109 9. LINEAR TRANSFORMATIONS: EXAMPLES AND APPLICATIONS 113 9.1 NUMERICAL EXAMPLES 113 9.2 SOME APPLICATIONS 123 9.3 EXERCISES 124 10. LINEAR TRANSFORMATIONS AND MATRICES 129 10.1 LINEAR TRANSFORMATIONS AND MATRICES IN IR 3 129 10.2 SOME NUMERICAL EXAMPLES 134 10.3 MATRICES AND THEIR ALGEBRA -,.... 136 10.4 SPECIAL TYPES OF MATRICES 141 10.5 EXERCISES 151 11. REPRESENTING LINEAR TRANSFORMATIONS BY MATRICES 159 11.1 REPRESENTING A LINEAR TRANSFORMATION BY A MATRIX .. 159 11.2 BASIC THEOREMS 165 11.3 CHANGE OF BASES 174 11.4 EXERCISES 178 12. MORE ON REPRESENTING LINEAR TRANSFORMATIONS BY MATRICES 185 12.1 PROJECTIONS 185 CONTENTS XI 12.2 NILPOTENT TRANSFORMATIONS 191 12.3 CYCLIC TRANSFORMATIONS 193 12.4 EXERCISES 195 13. SYSTEMS OF LINEAR EQUATIONS 199 13.1 EXISTENCE THEOREMS 201 13.2 REDUCTION TO ECHELON FORM 209 13.3 THE SIMPLEX METHOD 216 13.4 EXERCISES 224 14. THE ELEMENTS OF EIGENVALUE AND EIGENVECTOR THEORY 227 14.1 THE RANK OF AN ENDOMORPHISM 227 14.2 EIGENVALUES AND EIGENVECTORS 230 14.3 DETERMINANTS 238 14.4 THE CHARACTERISTIC POLYNOMIAL 245 14.5 DIAGONALIZATION THEOREMS 253 14.6 EXERCISES 260 15. INNER PRODUCT SPACES 267 15.1 SCALAR PRODUCTS 268 15.2 INNER PRODUCT SPACES 274 15.3 ISOMETRIES 288 15.4 THE RIESZ REPRESENTATION THEOREM 291 15.5 LEGENDRE POLYNOMIALS 298 15.6 EXERCISES 301 16. THE SPECTRAL THEOREM AND QUADRATIC FORMS 307 16.1 SELF-ADJOINT TRANSFORMATIONS 308 16.2 THE SPECTRAL THEOREM 316 16.3 THE PRINCIPAL AXIS THEOREM FOR QUADRATIC FORMS ... 324 16.4 A PROOF OF THE SPECTRAL THEOREM IN THE GENERAL CASE 335 16.5 EXERCISES 338 17. JORDAN CANONICAL FORM 343 17.1 INVARIANT SUBSPACES ; 345 17.2 NILPOTENT TRANSFORMATIONS 350 17.3 THE JORDAN NORMAL FORM 357 17.4 SQUARE ROOTS 372 17.5 THE HAMILTON-CAYLEY THEOREM 374 17.6 INVERSES 376 17.7 EXERCISES : 377 XII CONTENTS 18. APPLICATION TO DIFFERENTIAL EQUATIONS 381 18.1 LINEAR DIFFERENTIAL SYSTEMS: BASIC DEFINITIONS 381 18.2 DIAGONALIZABLE SYSTEMS 386 18.3 APPLICATION OF JORDAN FORM 395 18.4 EXERCISES 402 19. THE SIMILARITY PROBLEM 405 19.1 THE FUNDAMENTAL PROBLEM OF LINEAR ALGEBRA 405 19.2 A BIT OF INVARIANT THEORY 406 19.3 EXERCISES 409 A. MULTILINEAR ALGEBRA AND DETERMINANTS 411 A.1 MULTILINEAR FORMS. 411 A.2 DETERMINANTS 415 A.3 EXERCISES 428 B. COMPLEX NUMBERS 433 B.I THE COMPLEX NUMBERS 433 B.2 EXERCISES 441 FONT USAGE 443 NOTATIONS 445 INDEX 447
any_adam_object	1
author	Smith, Larry
author_facet	Smith, Larry
author_role	aut
author_sort	Smith, Larry
author_variant	l s ls
building	Verbundindex
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ctrlnum	(OCoLC)845055308 (DE-599)BVBBV012097903
dewey-full	512.5
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	512 - Algebra
dewey-raw	512.5
dewey-search	512.5
dewey-sort	3512.5
dewey-tens	510 - Mathematics
discipline	Mathematik
edition	3. ed.
format	Book
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isbn	0387984550
language	German
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publisher	Springer
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series2	Undergraduate texts in mathematics
spelling	Smith, Larry Verfasser aut Linear algebra Larry Smith 3. ed. New York [u.a.] Springer 1998 XII, 452 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Eigenwertproblem (DE-588)4013802-1 gnd rswk-swf Matrizengleichung (DE-588)4169125-8 gnd rswk-swf ALGOL (DE-588)4001182-3 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content (DE-588)4123623-3 Lehrbuch gnd-content Numerische Mathematik (DE-588)4042805-9 s Lineare Algebra (DE-588)4035811-2 s ALGOL (DE-588)4001182-3 s 1\p DE-604 Matrizengleichung (DE-588)4169125-8 s Numerisches Verfahren (DE-588)4128130-5 s 2\p DE-604 Eigenwertproblem (DE-588)4013802-1 s 3\p DE-604 4\p DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008192870&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Smith, Larry Linear algebra Eigenwertproblem (DE-588)4013802-1 gnd Matrizengleichung (DE-588)4169125-8 gnd ALGOL (DE-588)4001182-3 gnd Numerische Mathematik (DE-588)4042805-9 gnd Lineare Algebra (DE-588)4035811-2 gnd Numerisches Verfahren (DE-588)4128130-5 gnd
subject_GND	(DE-588)4013802-1 (DE-588)4169125-8 (DE-588)4001182-3 (DE-588)4042805-9 (DE-588)4035811-2 (DE-588)4128130-5 (DE-588)4151278-9 (DE-588)4123623-3
title	Linear algebra
title_auth	Linear algebra
title_exact_search	Linear algebra
title_full	Linear algebra Larry Smith
title_fullStr	Linear algebra Larry Smith
title_full_unstemmed	Linear algebra Larry Smith
title_short	Linear algebra
title_sort	linear algebra
topic	Eigenwertproblem (DE-588)4013802-1 gnd Matrizengleichung (DE-588)4169125-8 gnd ALGOL (DE-588)4001182-3 gnd Numerische Mathematik (DE-588)4042805-9 gnd Lineare Algebra (DE-588)4035811-2 gnd Numerisches Verfahren (DE-588)4128130-5 gnd
topic_facet	Eigenwertproblem Matrizengleichung ALGOL Numerische Mathematik Lineare Algebra Numerisches Verfahren Einführung Lehrbuch
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008192870&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT smithlarry linearalgebra

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