Linear algebra pure & applied
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
2014
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| 020 | |a 9814508365 |9 981-4508-36-5 | ||
| 020 | |a 9789814508377 |9 978-981-4508-37-7 | ||
| 020 | |a 9814508373 |9 981-4508-37-3 | ||
| 035 | |a (OCoLC)882966735 | ||
| 035 | |a (DE-599)BVBBV042384244 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
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| 049 | |a DE-739 |a DE-91G | ||
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| 082 | 0 | |a 512/.5 |2 23 | |
| 084 | |a SK 200 |0 (DE-625)143223: |2 rvk | ||
| 084 | |a MAT 150f |2 stub | ||
| 100 | 1 | |a Goodaire, Edgar G. |e Verfasser |0 (DE-588)133185702 |4 aut | |
| 245 | 1 | 0 | |a Linear algebra |b pure & applied |c Edgar G Goodaire |
| 264 | 1 | |c 2014 | |
| 300 | |a XVI, 716 S. |b Ill., graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Algebras, Linear |v Textbooks | |
| 650 | 0 | 7 | |a Lineare Algebra |0 (DE-588)4035811-2 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Lineare Algebra |0 (DE-588)4035811-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027820263&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-027820263 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0104 MAT 150f 2016 B 1005 0303 MAT 150f 2016 L 210 |
|---|---|
| DE-BY-TUM_katkey | 2189479 |
| DE-BY-TUM_location | 01 03 |
| DE-BY-TUM_media_number | 040008021327 040008021292 040008021281 040008021316 040008021305 040008021338 |
| _version_ | 1820852047369469952 |
| adam_text | Contents
Preface
bc
To My Students
xiii
Suggested Lecture Schedule
xv
1
Euclidean
η
-Space
ł
1.1
Vectors and Arrows
.........................., 1
1.2
Length and Direction
.......................... 26
1.3
Lines, Planes and the Cross Product
................. 43
1.4
Projections
................................ 66
1.5
Linear Dependence and Independence
............... 77
Review Exercises
............................. 84
2
Matrices and Linear Equations
93
2.1
The Algebra of Matrices
........................ 93
2.2
Application: Generating Codes with Matrices
...........121
2.3
Inverse and Transpose
.........................127
2.4
Systems of Linear Equations
...................... 141
2.5
Application: Electric Circuits
.....................169
2.6
Homogeneous Systems; Linear Independence
...........177
2.7
Elementary Matrices and
LU
Factorization
.............
18S
2.8
LDU Factorization
............................ 207
2.9
More on the Inverse of a Matrix
....................216
Review Exercises
............................. 228
3
Determinants, Eigenvalues, Eigenvectors
237
3.1
The Determinant of a Matrix
..................... 23/
3.2
Properties of Determinants
......................248
vi
Contents
3.3
Application:
Graphs
........................... 269
3.4
Eigenvalues and Eigenvectors
..................... 279
3.5
Similarity and Diagonalization
.................... 292
3.6
Application: Linear Recurrence Relations
.............. 306
3.7
Application: Markov Chains
...................... 311
Review Exercises
............................ . 325
4
Vector Spaces
331
4.1
The Theory of Linear Equations
.................... 331
4.2
Subspaces
................................. 347
4.3
Basis and Dimension
.......................... 361
4.4
Finite Dimensional Vector Spaces
.................. 370
4.5
One-sided Inverses
........................... 388
Review Exercises
............................. 396
5
Linear Transformations
401
5.1
Fundamentals
...............................401
5.2
Matrix Multiplication Revisited
....................415
5.3
Application: Computer Graphics
...................423
5.4
The Matrices of a Linear Transformation
..............428
5.5
Changing Coordinates
.........................441
Review Exercises
.............................458
6
Orthogonality
461
6.1
Projection Matrices
...........................461
6.2
Application: Data Fitting
........................480
6.3
The Gram-Schmidt Algorithm and QR Factorization
.......486
6.4
Orthogonal Subspaces and Complements
............ . 503
6.5
The
Pseudoinverse
of a Matrix
................... . 524
Review Exercises
............................. 535
7
The Spectral Theorem
541
7.1
Complex Vectors and Matrices
.................... 541
7.2
Unitary Diagonalization
......................., 554
7.3
Real Symmetric Matrices
........................ 570
7.4
Application: Quadratic Forms, Conic Sections
........... 576
7.5
The Singular Value Decomposition
.................. 581
Review Exercises
.......,..................... 589
Contents
Appendix
A: Complex Numbers
Appendix
В:
Show and Prove
Appendix C: Things I Must Remember
Answers to True/False and BB Exercises
Glossary
Index
|
| any_adam_object | 1 |
| author | Goodaire, Edgar G. |
| author_GND | (DE-588)133185702 |
| author_facet | Goodaire, Edgar G. |
| author_role | aut |
| author_sort | Goodaire, Edgar G. |
| author_variant | e g g eg egg |
| building | Verbundindex |
| bvnumber | BV042384244 |
| callnumber-first | Q - Science |
| callnumber-label | QA184 |
| callnumber-raw | QA184.2 |
| callnumber-search | QA184.2 |
| callnumber-sort | QA 3184.2 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 200 |
| classification_tum | MAT 150f |
| ctrlnum | (OCoLC)882966735 (DE-599)BVBBV042384244 |
| 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 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV042384244 |
| illustrated | Illustrated |
| indexdate | 2024-12-24T04:22:13Z |
| institution | BVB |
| isbn | 9789814508360 9814508365 9789814508377 9814508373 |
| language | English |
| lccn | 013022750 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027820263 |
| oclc_num | 882966735 |
| open_access_boolean | |
| owner | DE-739 DE-91G DE-BY-TUM |
| owner_facet | DE-739 DE-91G DE-BY-TUM |
| physical | XVI, 716 S. Ill., graph. Darst. 24 cm |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| record_format | marc |
| spellingShingle | Goodaire, Edgar G. Linear algebra pure & applied Algebras, Linear Textbooks Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4123623-3 |
| title | Linear algebra pure & applied |
| title_auth | Linear algebra pure & applied |
| title_exact_search | Linear algebra pure & applied |
| title_full | Linear algebra pure & applied Edgar G Goodaire |
| title_fullStr | Linear algebra pure & applied Edgar G Goodaire |
| title_full_unstemmed | Linear algebra pure & applied Edgar G Goodaire |
| title_short | Linear algebra |
| title_sort | linear algebra pure applied |
| title_sub | pure & applied |
| 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=027820263&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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