Introduction to linear algebra with applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
McGraw-Hill
2009
|
| Ausgabe: | 1. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes index. |
| Beschreibung: | XVIII, 488 S. Ill., graph. Darst. |
| ISBN: | 9780073532356 0073532355 |
Internformat
MARC
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| 245 | 1 | 0 | |a Introduction to linear algebra with applications |c James DeFranza ; Daniel Gagliardi |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Boston [u.a.] |b McGraw-Hill |c 2009 | |
| 300 | |a XVIII, 488 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes index. | ||
| 650 | 4 | |a Algebras, Linear |v Textbooks | |
| 650 | 4 | |a Algebras, Linear |v Problems, exercises, etc | |
| 650 | 0 | 7 | |a Lineare Algebra |0 (DE-588)4035811-2 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4151278-9 |a Einführung |2 gnd-content | |
| 689 | 0 | 0 | |a Lineare Algebra |0 (DE-588)4035811-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Gagliardi, Daniel |e Sonstige |4 oth | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016769127&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016769127 | ||
Datensatz im Suchindex
| _version_ | 1804138063318745088 |
|---|---|
| adam_text | Contents
Preface
ix
CHAPTER
1
Systems of Linear Equations and Matrices
1
1.1
Systems of Linear Equations
2
Exercise Set
1.1 12
1.2
Matrices and Elementary Row Operations
14
Exercise Set
1.2 23
1.3
Matrix Algebra
26
Exercise Set
1.3 37
1.4
The Inverse of a Square Matrix
39
Exercise Set
1.4 45
1.5
Matrix Equations
48
Exercise Set
1.5 51
1.6
Determinants
54
Exercise Set
1.6 65
1.7
Elementary Matrices and
LU
Factorization
68
Exercise Set
1.7 77
1.8
Applications of Systems of Linear Equations
79
Exercise Set
1.8 84
Review Exercises
89
Chapter Test
90
chapter
2
Linear Combinations and Linear Independence
93
2.1
Vectors in U
94
Exercise Set
2.1 99
2.2
Linear Combinations
Exercise Set
2.2 108
23
Linear Independence
Exercise Set
2.3 120
Review Exercises
123
Chapter Test
125
101
111
vi
Contents
vii
chapter
3
Vector Spaces
127
3.1
Definition of a Vector Space
129
Exercise Set
3.1 137
3.2
Subspaces
140
Exercise Set
3.2 154
3.3
Basis and Dimension
156
Exercise Set
3.3 171
3.4
Coordinates and Change of Basis
173
Exercise Set
3.4 182
3.5
Application: Differential Equations
185
Exercise Set
3.5 193
Review Exercises
194
Chapter Test
195
chapter
4
Linear Transformations
199
4.1
Linear Transformations
200
Exercise Set
4.1 211
4.2
The Null Space and Range
214
Exercise Set
4.2 223
4.3
Isomorphisms
226
Exercise Set
4.3 233
4.4
Matrix Representation of a Linear Transformation
235
Exercise Set
4.4 245
4.5
Similarity
249
Exercise Set
4.5 253
4.6
Application: Computer Graphics
255
Exercise Set
4.6 268
Review Exercises
270
Chapter Test
272
chapter
5
Eigenvalues and Eigenvectors
275
276
5.1
Eigenvalues and Eigenvectors
Exercise Set
5.1 285
5.2
Diagonalization
287
Exercise Set
5.2 298
5.3
Application: Systems of Linear Differential Equations
Exercise Set
5.3 309
300
viii Contents
5.4
Application:
Markov Chains
310
Exercise Set
5.4 315
Review Exercises
316
Chapter Test
318
chapter
О
Inner Product Spaces
321
6.1
The Dot Product on R
323
Exercise Set
6.1 331
6.2
Inner Product Spaces
333
Exercise Set
6.2 341
6.3
Orthonormal
Bases
342
Exercise Set
6.3 352
6.4
Orthogonal Complements
355
Exercise Set
6.4 364
6.5
Application: Least Squares Approximation
366
Exercise Set
6.5 375
6.6
Diagonalization of Symmetric Matrices
377
Exercise Set
6.6 383
6.7
Application: Quadratic Forms
385
Exercise Set
6.7 392
6.8
Application: Singular Value Decomposition
392
Exercise Set
6.8 403
Review Exercises
404
Chapter Test
406
Appendix
409
Answers to Odd-Numbered Exercises
440
Index
479
|
| adam_txt |
Contents
Preface
ix
CHAPTER
1
Systems of Linear Equations and Matrices
1
1.1
Systems of Linear Equations
2
Exercise Set
1.1 12
1.2
Matrices and Elementary Row Operations
14
Exercise Set
1.2 23
1.3
Matrix Algebra
26
Exercise Set
1.3 37
1.4
The Inverse of a Square Matrix
39
Exercise Set
1.4 45
1.5
Matrix Equations
48
Exercise Set
1.5 51
1.6
Determinants
54
Exercise Set
1.6 65
1.7
Elementary Matrices and
LU
Factorization
68
Exercise Set
1.7 77
1.8
Applications of Systems of Linear Equations
79
Exercise Set
1.8 84
Review Exercises
89
Chapter Test
90
chapter
2
Linear Combinations and Linear Independence
93
2.1
Vectors in U"
94
Exercise Set
2.1 99
2.2
Linear Combinations
Exercise Set
2.2 108
23
Linear Independence
Exercise Set
2.3 120
Review Exercises
123
Chapter Test
125
101
111
vi
Contents
vii
chapter
3
Vector Spaces
127
3.1
Definition of a Vector Space
129
Exercise Set
3.1 137
3.2
Subspaces
140
Exercise Set
3.2 154
3.3
Basis and Dimension
156
Exercise Set
3.3 171
3.4
Coordinates and Change of Basis
173
Exercise Set
3.4 182
3.5
Application: Differential Equations
185
Exercise Set
3.5 193
Review Exercises
194
Chapter Test
195
chapter
4
Linear Transformations
199
4.1
Linear Transformations
200
Exercise Set
4.1 211
4.2
The Null Space and Range
214
Exercise Set
4.2 223
4.3
Isomorphisms
226
Exercise Set
4.3 233
4.4
Matrix Representation of a Linear Transformation
235
Exercise Set
4.4 245
4.5
Similarity
249
Exercise Set
4.5 253
4.6
Application: Computer Graphics
255
Exercise Set
4.6 268
Review Exercises
270
Chapter Test
272
chapter
5
Eigenvalues and Eigenvectors
275
276
5.1
Eigenvalues and Eigenvectors
Exercise Set
5.1 285
5.2
Diagonalization
287
Exercise Set
5.2 298
5.3
Application: Systems of Linear Differential Equations
Exercise Set
5.3 309
300
viii Contents
5.4
Application:
Markov Chains
310
Exercise Set
5.4 315
Review Exercises
316
Chapter Test
318
chapter
О
Inner Product Spaces
321
6.1
The Dot Product on R"
323
Exercise Set
6.1 331
6.2
Inner Product Spaces
333
Exercise Set
6.2 341
6.3
Orthonormal
Bases
342
Exercise Set
6.3 352
6.4
Orthogonal Complements
355
Exercise Set
6.4 364
6.5
Application: Least Squares Approximation
366
Exercise Set
6.5 375
6.6
Diagonalization of Symmetric Matrices
377
Exercise Set
6.6 383
6.7
Application: Quadratic Forms
385
Exercise Set
6.7 392
6.8
Application: Singular Value Decomposition
392
Exercise Set
6.8 403
Review Exercises
404
Chapter Test
406
Appendix
409
Answers to Odd-Numbered Exercises
440
Index
479 |
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| indexdate | 2024-07-09T21:22:14Z |
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| isbn | 9780073532356 0073532355 |
| language | English |
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| spelling | DeFranza, James 1950- Verfasser (DE-588)140094210 aut Introduction to linear algebra with applications James DeFranza ; Daniel Gagliardi 1. ed. Boston [u.a.] McGraw-Hill 2009 XVIII, 488 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes index. Algebras, Linear Textbooks Algebras, Linear Problems, exercises, etc 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 Gagliardi, Daniel Sonstige oth Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016769127&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | DeFranza, James 1950- Introduction to linear algebra with applications Algebras, Linear Textbooks Algebras, Linear Problems, exercises, etc Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4151278-9 |
| title | Introduction to linear algebra with applications |
| title_auth | Introduction to linear algebra with applications |
| title_exact_search | Introduction to linear algebra with applications |
| title_exact_search_txtP | Introduction to linear algebra with applications |
| title_full | Introduction to linear algebra with applications James DeFranza ; Daniel Gagliardi |
| title_fullStr | Introduction to linear algebra with applications James DeFranza ; Daniel Gagliardi |
| title_full_unstemmed | Introduction to linear algebra with applications James DeFranza ; Daniel Gagliardi |
| title_short | Introduction to linear algebra with applications |
| title_sort | introduction to linear algebra with applications |
| topic | Algebras, Linear Textbooks Algebras, Linear Problems, exercises, etc Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Algebras, Linear Textbooks Algebras, Linear Problems, exercises, etc Lineare Algebra Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016769127&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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