Linear algebra:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
McGraw-Hill Education
[2018]
|
| Ausgabe: | Sixth edition |
| Schriftenreihe: | Schaum's outlines
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030280217&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | VI, 425 Seiten Diagramme |
| ISBN: | 9781260011449 1260011445 |
Internformat
MARC
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| 245 | 1 | 0 | |a Linear algebra |c Seymour Lipschutz, PhD, Temple University, Marc Lars Lipson, PhD, University of Virginia |
| 246 | 1 | 3 | |a Schaum's outlines Linear Algebra |
| 250 | |a Sixth edition | ||
| 264 | 1 | |a New York |b McGraw-Hill Education |c [2018] | |
| 300 | |a VI, 425 Seiten |b Diagramme | ||
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| 338 | |b nc |2 rdacarrier | ||
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| 650 | 4 | |a Algebras, Linear / Problems, exercises, etc | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
List of Symbols iv
CHAPTER 1 Vectors in R and C , Spatial Vectors 1
1.1 Introduction 1.2 Vectors in R 1.3 Vector Addition and Scalar Multi-
plication 1.4 Dot (Inner) Product 1.5 Located Vectors, Hyperplanes, Lines,
Curves in Rn 1.6 Vectors in R3 (Spatial Vectors), ijk Notation 1.7 Complex
Numbers 1.8 Vectors in C
CHAPTER 2 Algebra of Matrices 27
2.1 Introduction 2.2 Matrices‘2.3 Matrix Addition and Scalar Multiplica-
tion 2.4 Summation Symbol 2.5 Matrix Multiplication 2.6 Transpose of a
Matrix 2.7 Square Matrices 2.8 Powers of Matrices, Polynomials in
Matrices 2.9 Invertible (Nonsingular) Matrices 2.10 Special Types of ,
Square Matrices 2.11 Complex Matrices 2.12 Block Matrices ’ . . : “ ’
CHAPTER 3 « Systems of Linear Equations - 57
3.1 Introduction 3.2 Basic Definitions, Solutions 3.3 Equiváleiit Systems,
Elementary Operations 3.4 Small Square Systems of Linear Equations 3.5
Systems in Triangular and Echelon Forms 3.6 Gaussian Elimination 3.7
Echelon Matrices, Row Canonical Form, Row Equivalence 3.8 Gaussian’ *
Elimination, Matrix Formulation 3.9 Matrix Equation of a System of Linear
Equations 3.10 Systems of Linear Equations and Linear Combinations of
Vectors 3.11 Homogeneous Systems of Linear Equations 3.12 Elementary
Matrices 3.13 LU Decomposition
CHAPTER 4 Vector Spaces : 112
4.1 Introduction 4.2 Vector Spaces 4.3 Examples of. Vector Spaces 4.4
Linear Combinations, Spanning Sets 4.5 Subspaces 4.6 Linear Spans, Row
Space of a Matrix 4.7 Linear Dependence and Independence 4.8 Basis and
Dimension 4.9 Application to Matrices, Rank of a Matrix 4.10 Sums and
Direct Sums 4.11 Coordinates 4.12 Isomorphism of V, and Kn 4.13 Full
Rank Factorization 4.14 Generalized (Moore-Penrose)Jnverse 4.15 Least-
Square Solution • 1 .}. ■ , r
CHAPTER 5 Linear Mappings 166
5.1 Introduction 5.2 Mappings, Functions^.3 Linear Mappings (Linear
Transformations) 5.4 Kernel and Image of a Linear Mapping 5.5 Singular
and Nonsingular Linear Mappings, Isomorphisms 5.6 Operations with
Linear Mappings 5.7 Algebra A(V) of Linear Operators : f... V*.:.’-
CHAPTER 6 Linear Mappings and Matrices 197
6.1 Introduction 6.2 Matrix Representation of a Linear Operator 6.3 Change
of Basis 6.4 Similarity 6.5 Matrices and General Linear Mappings
CHAPTER 7 Inner Product Spaces, Orthogonality 228
7.1 Introduction 7.2 Inner Product Spaces 7.3 Examplés of Inner Product
Spaces 7.4 Cauchy-Schwarz Inequality, Applications 7.5 Orthogonal-,
ity 7.6 Orthogonal Sets and Bases 7.7 Gram-Schmidt Orthogonalization
V
VI
Contents
CHAPTER 8
CHAPTER 9
CHAPTER 10
CHAPTER 11
CHAPTER 12
CHAPTER 13
APPENDIX A
APPENDIX B
APPENDIX C
APPENDIX D
Process 7.8 Orthogonal and Positive Definite Matrices 7.9 Complex Inner
Product Spaces 7.10 Normed Vector Spaces (Optional)
Determinants 266
8.1 Introduction 8.2 Determinants of Orders 1 and 2 8.3 Determinants of
Order 3 8.4 Permutations 8.5 Determinants of Arbitrary Order 8.6 Proper-
ties of Determinants 8.7 Minors and Cofactors 8.8 Evaluation of Determi-
nants 8.9 Classical Adjoint 8.10 Applications to Linear Equations, Cramer’s
Rule 8.11 Submatrices, Minors, Principal Minors 8.12 Block Matrices and
Determinants 8.13 Determinants and Volume 8.14 Determinant of a Linear
Operator 8.15 Multilinearity and Determinants
Diagonalization: Eigenvalues and Eigenvectors 294
9.1 Introduction 9.2 Polynomials of Matrices 9.3 Characteristic Polynomial,
Cayley-Hamilton Theorem 9.4 Diagonalization, Eigenvalues and Eigenvec-
tors 9.5 Computing Eigenvalues and Eigenvectors, Diagonalizing Matrices 9.6
Diagonalizing Real Symmetric Matrices and Quadratic Forms 9.7 Minimal
Polynomial 9.8 Characteristic and Minimal Polynomials of Block Matrices
Canonical Forms 327
10.1 Introduction 10.2 Triangular Form 10.3 Invariance 10.4 Invariant
Direct-Sum Decompositions 10.5 Primary Decomposition 10.6 Nilpotent
Operators 10.7 Jordan Canonical Form 10.8 Cyclic Subspaces 10.9
Rational Canonical Form 10.10 Quotient Spaces
Linear Functionals and the Dual Space 351
11.1 Introduction 11.2 Linear Functionals and the Dual Space 11.3 Dual
Basis 11.4 Second Dual Space 11.5 Annihilators 11.6 Transpose of a
Linear Mapping
Bilinear, Quadratic, and Hermitian Forms 361
12.1 Introduction 12.2 Bilinear Forms 12.3 Bilinear Forms and
Matrices 12.4 Alternating Bilinear Forms 12.5 Symmetric Bilinear Forms,
Quadratic Forms 12.6 Real Symmetric Bilinear Forms, Law of Inertia 12.7
Hermitian Forms
Linear Operators on Inner Product Spaces 379
13.1 Introduction 13.2 Adjoint Operators 13.3 Analogy Between A(V) and
C, Special Linear Operators 13.4 Self-Adjoint Operators 13.5 Orthogonal
and Unitary Operators 13.6 Orthogonal and Unitary Matrices 13.7 Change
of Orthonormal Basis 13.8 Positive Definite and Positive Operators 13.9
Diagonalization and Canonical Forms in Inner Product Spaces 13.10 Spec-
tral Theorem
Multilinear Products 398
Algebraic Structures 405
Polynomials over a Field 413
Odds and Ends 417
Index
421
|
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| author_GND | (DE-588)140841733 (DE-588)123331730 |
| author_facet | Lipschutz, Seymour Lipson, Marc |
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| bvnumber | BV044886110 |
| classification_rvk | SK 220 |
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| discipline | Mathematik |
| edition | Sixth edition |
| format | Book |
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| id | DE-604.BV044886110 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T18:13:18Z |
| institution | BVB |
| isbn | 9781260011449 1260011445 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030280217 |
| oclc_num | 1031044247 |
| open_access_boolean | |
| owner | DE-29T DE-20 DE-703 DE-739 DE-11 DE-862 DE-BY-FWS |
| owner_facet | DE-29T DE-20 DE-703 DE-739 DE-11 DE-862 DE-BY-FWS |
| physical | VI, 425 Seiten Diagramme |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | McGraw-Hill Education |
| record_format | marc |
| series2 | Schaum's outlines |
| spellingShingle | Lipschutz, Seymour Lipson, Marc Linear algebra Algebras, Linear / Outlines, syllabi, etc Algebras, Linear / Problems, exercises, etc Algebras, Linear fast Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4035811-2 |
| title | Linear algebra |
| title_alt | Schaum's outlines Linear Algebra |
| title_auth | Linear algebra |
| title_exact_search | Linear algebra |
| title_full | Linear algebra Seymour Lipschutz, PhD, Temple University, Marc Lars Lipson, PhD, University of Virginia |
| title_fullStr | Linear algebra Seymour Lipschutz, PhD, Temple University, Marc Lars Lipson, PhD, University of Virginia |
| title_full_unstemmed | Linear algebra Seymour Lipschutz, PhD, Temple University, Marc Lars Lipson, PhD, University of Virginia |
| title_short | Linear algebra |
| title_sort | linear algebra |
| topic | Algebras, Linear / Outlines, syllabi, etc Algebras, Linear / Problems, exercises, etc Algebras, Linear fast Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Algebras, Linear / Outlines, syllabi, etc Algebras, Linear / Problems, exercises, etc Algebras, Linear Lineare Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030280217&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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