Linear algebra and its applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston ; Munich [u.a.]
Pearson/Addison-Wesley
2006
|
| Ausgabe: | 3. ed. update, internat. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 576 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 0321287134 0321314859 |
Internformat
MARC
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| 100 | 1 | |a Lay, David C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Linear algebra and its applications |c David C. Lay |
| 246 | 1 | 3 | |a Linear algebra |
| 250 | |a 3. ed. update, internat. ed. | ||
| 264 | 1 | |a Boston ; Munich [u.a.] |b Pearson/Addison-Wesley |c 2006 | |
| 300 | |a 576 S. |b Ill., graph. Darst. |e 1 CD-ROM (12 cm) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Algebras, Linear |v Textbooks | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-022535047 | ||
Datensatz im Suchindex
| _version_ | 1804145667720871936 |
|---|---|
| adam_text | Солїєлїб
CHAPTER
1
Preface
9
A Note to Students
15
Linear Equations in Linear Algebra
17
introductory example: Linear Models in Economics
and Engineering
17
1.1
Systems of Linear Equations
18
1.2
Row Reduction and Echelon Forms
30
1.3
Vector Equations
44
1.4
The Matrix Equation Ax
=
b
56
1.5
Solution Sets of Linear Systems
66
1.6
Applications of Linear Systems
73
1.7
Linear Independence
81
1.8
Introduction to Linear Transformations
89
1.9
The Matrix of a Linear Transformation
98
1.10
Linear Models in Business, Science, and Engineering
Supplementary Exercises
118
108
chapter
2
IVI a
trix Algebra
121
introductory EXAMPLE: Computer Models in Aircraft
Design
121
2.1
Matrix Operations
123
2.2
The Inverse of a Matrix
134
2.3
Characterizations of Invertible Matrices
144
2.4
Partitioned Matrices
150
2.5
Matrix Factorizations
158
2.6
The
Leontief
Input-Output Model
168
Contents
ММИНММММКЯП!
CHAPTER
3
CHAPTER
4
2.7
Applications to Computer Graphics
174
2.8
SubspacesofE
183
2.9
Dimension and Rank
192
Supplementary Exercises
199
Determinants
201
introductory example: Determinants in Analytic Geometry
3.1
Introduction to Determinants
202
3.2
Properties of Determinants
208
3.3
Cramer s Rule, Volume, and Linear Transformations
217
Supplementary Exercises
227
Vector Spaces
231
introductory example: Space Flight and Control Systems
4.1
Vector Spaces and Subspaces
232
4.2
Null Spaces, Column Spaces, and Linear Transformations
242
4.3
Linearly Independent Sets; Bases
253
4.4
Coordinate Systems
262
4.5
The Dimension of a Vector Space
272
4.6
Rank
278
4.7
Change of Basis
287
4.8
Applications to Difference Equations
293
4.9
Applications to Markov Chains
304
Supplementary Exercises
314
chapters Eigenvalues and Eigenvectors
317
introductory example: Dynamical Systems
and Spotted Owls
317
5.1
Eigenvectors and Eigenvalues
318
5.2
The Characteristic Equation
326
5.3
Diagonalization
335
5.4
Eigenvectors and Linear Transformations
343
5.5
Complex Eigenvalues
351
5.6
Discrete Dynamical Systems
358
201
231
CHAPTER
6
CHAPTER
7
Contents
5.7
Applications to Differential Equations
369
5.8
Iterative Estimates for Eigenvalues
379
Supplementary Exercises
386
Orthogonality and Least Squares
389
introductory example: Readjusting the North American
Datum
389
6.1
Inner Product, Length, and Orthogonality
391
6.2
Orthogonal Sets
400
6.3
Orthogonal Projections
410
6.4
The Gram-Schmidt Process
418
6.5
Least-Squares Problems
425
6.6
Applications to Linear Models
435
6.7
Inner Product Spaces
443
6.8
Applications of Inner Product Spaces
452
Supplementary Exercises
460
Symmetric lVlatrices and Quadratic Forms
463
introductory example: Multichannel Image Processing
463
7.1
Diagonalization of Symmetric Matrices
465
7.2
Quadratic Forms
471
7.3
Constrained Optimization
479
7.4
The Singular Value Decomposition
487
7.5
Applications to Image Processing and Statistics
498
Supplementary Exercises
507
chapter
8
The Geometry of Vector Spaces
ONLINE ONLY introductory example: The Platonic Solids
8.1
Affine
Combinations
8.2
Affine
Independence
8.3
Convex Combinations
8.4
Hyperplanes
8.5
Polytopes
8.6
Curves and Surfaces
Contents
chapter
9
Optimization
ONLINE ONLY introductory example: The Berlin Airlift
9.1
Matrix Games
9.2
Linear Programming
—
Geometric Method
9.3
Linear Programming
—
Simplex Method
9.4
Duality
Appendixes
A Uniqueness of the Reduced Echelon Form
В
Complex Numbers
511
509
Glossary
517
Answers to Odd-Numbered Exercises
527
Index
565
|
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| 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. update, internat. ed. |
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| id | DE-604.BV037381942 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T23:23:06Z |
| institution | BVB |
| isbn | 0321287134 0321314859 |
| language | English |
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| physical | 576 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| publishDate | 2006 |
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| spelling | Lay, David C. Verfasser aut Linear algebra and its applications David C. Lay Linear algebra 3. ed. update, internat. ed. Boston ; Munich [u.a.] Pearson/Addison-Wesley 2006 576 S. Ill., graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Algebras, Linear Textbooks Lineare Algebra (DE-588)4035811-2 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Lineare Algebra (DE-588)4035811-2 s DE-604 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022535047&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lay, David C. Linear algebra and its applications Algebras, Linear Textbooks Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4123623-3 |
| title | Linear algebra and its applications |
| title_alt | Linear algebra |
| title_auth | Linear algebra and its applications |
| title_exact_search | Linear algebra and its applications |
| title_full | Linear algebra and its applications David C. Lay |
| title_fullStr | Linear algebra and its applications David C. Lay |
| title_full_unstemmed | Linear algebra and its applications David C. Lay |
| title_short | Linear algebra and its applications |
| title_sort | linear algebra and its applications |
| topic | Algebras, Linear Textbooks Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Algebras, Linear Textbooks Lineare Algebra Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022535047&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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