Linear algebra: concepts and methods
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2012
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XIV, 516 S. graph. Darst. 25 cm |
| ISBN: | 9780521279482 |
Internformat
MARC
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| 001 | BV039969573 | ||
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| 015 | |a GBB201833 |2 dnb | ||
| 020 | |a 9780521279482 |c pbk |9 978-0-521-27948-2 | ||
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| 100 | 1 | |a Anthony, Martin |d 1967- |e Verfasser |0 (DE-588)114372675 |4 aut | |
| 245 | 1 | 0 | |a Linear algebra |b concepts and methods |c Martin Anthony and Michele Harvey |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2012 | |
| 300 | |a XIV, 516 S. |b graph. Darst. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Algebras, Linear / Textbooks | |
| 650 | 0 | 7 | |a Lineare Algebra |0 (DE-588)4035811-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lehrbuch |0 (DE-588)4123623-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lineare Algebra |0 (DE-588)4035811-2 |D s |
| 689 | 0 | 1 | |a Lehrbuch |0 (DE-588)4123623-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Harvey, Michele |e Verfasser |0 (DE-588)1022768220 |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Bamberg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024827146&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-024827146 | ||
Datensatz im Suchindex
| _version_ | 1804148947643531264 |
|---|---|
| adam_text | Contents
Preface
page
xiii
Preliminaries: before we begin
1
Sets and set notation
1
Numbers
2
Mathematical terminology
3
Basic algebra
4
Trigonometry
7
A little bit of logic
8
1
Matrices and vectors
10
1.1
What is a matrix?
10
1.2
Matrix addition and scalar multiplication
11
1.3
Matrix multiplication
12
1.4
Matrix algebra
14
1.5
Matrix inverses
І6
1
.6
Powers of a matrix
20
1.7
The transpose and symmetric matrices
20
1.8
Vectors in Rn
23
1.9
Developing geometric insight
27
1.10
Lines
33
1.11
Planes in E3
39
1.12
Lines and
hyperplanes
in RH
46
1.13
Learning outcomes
47
1.14
Comments on activities
48
1.15
Exercises
53
1.16
Problems
55
viii Contents
2
Systems
of linear equations
59
2.1
Systems of linear equations
59
2.2
Row operations
62
2.3
Gaussian elimination
64
2.4
Homogeneous systems and null space
75
2.5
Learning outcomes
81
2.6
Comments on activities
82
2.7
Exercises
84
2.8
Problems
86
3
Matrix inversion and determinants
90
3.1
Matrix inverse using row operations
90
3.2
Determinants
98
3.3
Results on determinants
104
3.4
Matrix inverse using cofactors
113
3.5
Leontief
input-output analysis
119
3.6
Learning outcomes
121
3.7
Comments on activities
122
3.8
Exercises
125
3.9
Problems
128
4
Rank, range and linear equations
131
4.1
The rank of a matrix
131
4.2
Rank and systems of linear equations
133
4.3
Range
139
4.4
Learning outcomes
142
4.5
Comments on activities
142
4.6
Exercises
144
4.7
Problems
146
5
Vector spaces
149
5.1
Vector spaces
149
5.2
Subspaces
154
5.3
Linear span
160
5.4
Learning outcomes
164
5.5
Comments on activities
164
5.6
Exercises
5.7
Problems
6 Linear
independence, bases and dimension
6.1
Linear independence
6.2
Bases
6.3
Coordinates
6.4
Dimension
6.5
Basis and dimension in
Ш
6.6
Learning outcomes
6.7
Comments on activities
6.8
Exercises
6.9
Problems
Contents
ix
168
170
172
172
181
185
186
191
199
199
202
205
7
Linear transformations and change of basis
210
7.1
Linear transformations
210
7.2
Range and null space
220
7.3
Coordinate change
223
7.4
Change of basis and similarity
229
7.5
Learning outcomes
235
7.6
Comments on activities
235
7.7
Exercises
239
7.8
Problems
242
8
Diagonalisation
247
8.1
Eigenvalues and eigenvectors
247
8.2
Diagonalisation of a square matrix
256
8.3
When is diagonalisation possible?
263
8.4
Learning outcomes
272
8.5
Comments on activities
273
8.6
Exercises
274
8.7
Problems
276
9
Applications of diagonalisation
279
9.1
Powers of matrices
279
9.2
Systems of difference equations
282
Contents
9.3
Linear systems of differential equations
296
9.4
Learning outcomes
303
9.5
Comments on activities
303
9.6
Exercises
305
9.7
Problems
308
10 Inner
products and orthogonality
312
10.1
Inner products
312
10.2
Orthogonality
316
10.3
Orthogonal matrices
319
10.4
Gram-Schmidt
orthonormalisation
process
321
10.5
Learning outcomes
323
10.6
Comments on activities
324
10.7
Exercises
325
10.8
Problems
326
11 Orthogonal diagonalisation
and its applications
329
ИЛ
Orthogonal diagonalisation of symmetric matrices
329
11.2
Quadratic forms
339
11.3
Learning outcomes
355
11.4
Comments on activities
356
11.5
Exercises
358
11.6
Problems
360
12
Direct sums and projections
364
12.1
The direct sum of two subspaces
364
12.2
Orthogonal complements
367
12.3
Projections
372
12.4
Characterising projections and orthogonal
projections
374
12.5
Orthogonal projection onto the range of a matrix
376
12.6
Minimising the distance to a subspace
379
12.7
Fitting functions to data: least squares
approximation
380
12.8
Learning outcomes
383
12.9
Comments on activities
384
Contents xi
12.10
Exercises
385
12.11 Problems 386
13
Complex
matrices
and vector spaces
389
13.1
Complex numbers
389
13.2
Complex vector spaces
398
13.3
Complex matrices
399
13.4
Complex inner product spaces
401
13.5
Hermitian conjugates
407
13.6
Unitary diagonalisation and normal matrices
412
13.7
Spectral decomposition
415
13.8
Learning outcomes
420
13.9
Comments on activities
421
13.10
Exercises
424
13.11
Problems
426
Comments on exercises
431
Index
513
|
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| author | Anthony, Martin 1967- Harvey, Michele |
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| bvnumber | BV039969573 |
| classification_rvk | QH 140 SK 220 |
| classification_tum | MAT 150f |
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| 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 | 3512.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV039969573 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:15:14Z |
| institution | BVB |
| isbn | 9780521279482 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024827146 |
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| physical | XIV, 516 S. graph. Darst. 25 cm |
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| publisher | Cambridge Univ. Press |
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| spelling | Anthony, Martin 1967- Verfasser (DE-588)114372675 aut Linear algebra concepts and methods Martin Anthony and Michele Harvey 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2012 XIV, 516 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Algebras, Linear / Textbooks Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Lehrbuch (DE-588)4123623-3 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s Lehrbuch (DE-588)4123623-3 s DE-604 Harvey, Michele Verfasser (DE-588)1022768220 aut Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024827146&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Anthony, Martin 1967- Harvey, Michele Linear algebra concepts and methods Algebras, Linear / Textbooks Lineare Algebra (DE-588)4035811-2 gnd Lehrbuch (DE-588)4123623-3 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4123623-3 |
| title | Linear algebra concepts and methods |
| title_auth | Linear algebra concepts and methods |
| title_exact_search | Linear algebra concepts and methods |
| title_full | Linear algebra concepts and methods Martin Anthony and Michele Harvey |
| title_fullStr | Linear algebra concepts and methods Martin Anthony and Michele Harvey |
| title_full_unstemmed | Linear algebra concepts and methods Martin Anthony and Michele Harvey |
| title_short | Linear algebra |
| title_sort | linear algebra concepts and methods |
| title_sub | concepts and methods |
| topic | Algebras, Linear / Textbooks Lineare Algebra (DE-588)4035811-2 gnd Lehrbuch (DE-588)4123623-3 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=024827146&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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