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Linear algebra:

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Main Author:	Greub, Werner Hildbert 1925-1991 (Author)
Format:	Book
Language:	English
Published:	New York [u.a.] Springer 1975
Edition:	4. ed.
Series:	Graduate texts in mathematics 23
Subjects:	Algebra lineal Algèbre linéaire Lineaire algebra Algebras, Linear Lineare Algebra Einführung
Online Access:	Inhaltsverzeichnis
Physical Description:	XVI, 451 S.
ISBN:	0387901108 3540901108

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MARC


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adam_text	Contents Chapter 0. Prerequisites 1 Chapter I. Vector spaces 5 § 1. Vector spaces 5 §2. Linear mappings 16 § 3. Subspaces and factor spaces 22 § 4. Dimension 32 §5. The topology of a real finite dimensional vector space 37 Chapter II. Linear mappings 41 § 1. Basic properties 41 §2. Operations with linear mappings 51 § 3. Linear isomorphisms 55 § 4. Direct sum of vector spaces 56 § 5. Dual vector spaces 63 § 6. Finite dimensional vector spaces 76 Chapter III. Matrices 83 §1. Matrices and systems of linear equations 83 §2. Multiplication of matrices 89 § 3. Basis transformation 92 § 4. Elementary transformations 95 Chapter IV. Determinants 99 § 1. Determinant functions 99 § 2. The determinant of a linear transformation 104 §3. The determinant of a matrix 109 §4. Dual determinant functions 112 § 5. The adjoint matrix 114 §6. The characteristic polynomial 120 §7. The trace 126 §8. Oriented vector spaces 131 Chapter V. Algebras 144 §1. Basic properties 144 §2. Ideals 158 §3. Change of coefficient field of a vector space 163 Chapter VI. Gradations and homology 167 § 1. G graded vector spaces 167 §2. G graded algebras 174 § 3. Differential spaces and differential algebras 178 Chapter VII. Inner product spaces 186 § 1. The inner product 186 §2. Orthonormal bases 191 XVI Contents § 3. Normed determinant functions 195 § 4. Duality in an inner product space 202 § 5. Normed vector spaces 205 §6. The algebra of quaternions 208 Chapter VIII. Linear mappings of inner product spaces 216 §1. The adjoint mapping 216 § 2. ¦ Selfadjoint mappings 221 § 3. Orthogonal projections 226 § 4. Skew mappings 229 § 5. Isometric mappings 232 § 6. Rotations of Euclidean spaces of dimension 2, 3 and 4 237 § 7. Differentiable families of linear automorphisms 249 Chapter IX. Symmetric bilinear functions 261 §1. Bilinear and quadratic functions 261 § 2. The decomposition of £ 265 § 3. Pairs of symmetric bilinear functions 272 §4. Pseudo Euclidean spaces 281 § 5. Linear mappings of Pseudo Euclidean spaces 288 Chapter X. Quadrics 296 § 1. Affine spaces 296 § 2. Quadrics in the affine space 301 § 3. Affine equivalence of quadrics 310 §4. Quadrics in the Euclidean space 316 Chapter XI. Unitary spaces 325 §1. Hermitian functions 325 § 2. Unitary spaces 327 §3. Linear mappings of unitary spaces 334 § 4. Unitary mappings of the complex plane 340 § 5. Application to Lorentz transformations 345 Chapter XII. Polynomial algebra 351 §1. Basic properties 351 § 2. Ideals and divisibility 357 § 3. Factor algebras 366 §4. The structure of factor algebras 369 Chapter XIII. Theory of a linear transformation 383 § 1. Polynomials in a linear transformation 383 § 2. Generalized eigenspaces 390 §3. Cyclic spaces 397 § 4. Irreducible spaces 402 §5. Application of cyclic spaces 415 §6. Nilpotent and semisimple transformations 425 § 7. Applications to inner product spaces 436 Bibliography 445 Subject Index 447
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indexdate	2024-07-09T15:49:00Z
institution	BVB
isbn	0387901108 3540901108
language	English
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physical	XVI, 451 S.
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spelling	Greub, Werner Hildbert 1925-1991 Verfasser (DE-588)123729912 aut Lineare Algebra Linear algebra Werner Greub 4. ed. New York [u.a.] Springer 1975 XVI, 451 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 23 Algebra lineal Algèbre linéaire Lineaire algebra gtt Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Lineare Algebra (DE-588)4035811-2 s DE-604 Graduate texts in mathematics 23 (DE-604)BV000000067 23 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001754946&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Greub, Werner Hildbert 1925-1991 Linear algebra Graduate texts in mathematics Algebra lineal Algèbre linéaire Lineaire algebra gtt Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd
subject_GND	(DE-588)4035811-2 (DE-588)4151278-9
title	Linear algebra
title_alt	Lineare Algebra
title_auth	Linear algebra
title_exact_search	Linear algebra
title_full	Linear algebra Werner Greub
title_fullStr	Linear algebra Werner Greub
title_full_unstemmed	Linear algebra Werner Greub
title_short	Linear algebra
title_sort	linear algebra
topic	Algebra lineal Algèbre linéaire Lineaire algebra gtt Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd
topic_facet	Algebra lineal Algèbre linéaire Lineaire algebra Algebras, Linear Lineare Algebra Einführung
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volume_link	(DE-604)BV000000067
work_keys_str_mv	AT greubwernerhildbert linearealgebra AT greubwernerhildbert linearalgebra

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