Linear algebra and matrix theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
1970
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 352 S. |
Staff View
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Record in the Search Index
| _version_ | 1804135866256326656 |
|---|---|
| adam_text | Contents
Introduction 1
I Vector spaces 5
1. Definitions 5
2. Linear Independence and Linear Dependence 10
3. Bases of Vector Spaces 15
4. Subspaces 20
II Linear transformations and matrices 26
1. Linear Transformations 27
2. Matrices 37
3. Non Singular Matrices 45
4. Change of Basis 50
5. Hermite Normal Form 53
6. Elementary Operations and Elementary Matrices 57
7. Linear Problems and Linear Equations 63
8. Other Applications of the Hermite Normal Form 68
9. Normal Forms 74
*10. Quotient Sets, Quotient Spaces 78
*11. Hom(U, V) 83
III Determinants, eigenvalues, and similarity transformations 85
1. Permutations 86
2. Determinants 89
3. Cofactors 93
4. The Hamilton Cayley Theorem 98
5. Eigenvalues and Eigenvectors 104
6. Some Numerical Examples 110
7. Similarity 113
*8. The Jordan Normal Form 118
IV Linear functionals, bilinear forms, quadratic forms 128
1. Linear Functionals 129
2. Duality 133
xi
xii Contents
3. Change of Basis 134
4. Annihilators 138
5. The Dual of a Linear Transformation 142
*6. Duality of Linear Transformations 145
*7. Direct Sums 147
8. Bilinear Forms 156
9. Quadratic Forms 160
10. The Normal Form 162
11. Real Quadratic Forms 168
12. Hermitian Forms 170
V Orthogonal and unitary transformations, normal matrices 175
1. Inner Products and Orthonormal Bases 176
*2. Complete Orthonormal Sets 182
3. The Representation of a Linear Functional by an Inner Product 186
4. The Adjoint Transformation 189
5. Orthogonal and Unitary Transformations 194
6. Orthogonal and Unitary Matrices 195
7. Superdiagonal Form 199
8. Normal Matrices 201
9. Normal Linear Transformations 203
10. Hermitian and Unitary Matrices 208
11. Real Vector Spaces 209
12. The Computational Processes 213
VI Selected applications of linear algebra 219
1. Vector Geometry 220
2. Finite Cones and Linear Inequalities 229
3. Linear Programming 239
4. Applications to Communication Theory 253
5. Vector Calculus 259
6. Spectral Decomposition of Linear Transformations 270
7. Systems of Linear Differential Equations 278
8. Small Oscillations of Mechanical Systems 284
9. Representations of Finite Groups by Matrices 292
10. Application of Representation Theory to Symmetric Mechanical
Systems 312
Appendix 319
Answers to selected exercises 325
Index 345
|
| adam_txt |
Contents
Introduction 1
I Vector spaces 5
1. Definitions 5
2. Linear Independence and Linear Dependence 10
3. Bases of Vector Spaces 15
4. Subspaces 20
II Linear transformations and matrices 26
1. Linear Transformations 27
2. Matrices 37
3. Non Singular Matrices 45
4. Change of Basis 50
5. Hermite Normal Form 53
6. Elementary Operations and Elementary Matrices 57
7. Linear Problems and Linear Equations 63
8. Other Applications of the Hermite Normal Form 68
9. Normal Forms 74
*10. Quotient Sets, Quotient Spaces 78
*11. Hom(U, V) 83
III Determinants, eigenvalues, and similarity transformations 85
1. Permutations 86
2. Determinants 89
3. Cofactors 93
4. The Hamilton Cayley Theorem 98
5. Eigenvalues and Eigenvectors 104
6. Some Numerical Examples 110
7. Similarity 113
*8. The Jordan Normal Form 118
IV Linear functionals, bilinear forms, quadratic forms 128
1. Linear Functionals 129
2. Duality 133
xi
xii Contents
3. Change of Basis 134
4. Annihilators 138
5. The Dual of a Linear Transformation 142
*6. Duality of Linear Transformations 145
*7. Direct Sums 147
8. Bilinear Forms 156
9. Quadratic Forms 160
10. The Normal Form 162
11. Real Quadratic Forms 168
12. Hermitian Forms 170
V Orthogonal and unitary transformations, normal matrices 175
1. Inner Products and Orthonormal Bases 176
*2. Complete Orthonormal Sets 182
3. The Representation of a Linear Functional by an Inner Product 186
4. The Adjoint Transformation 189
5. Orthogonal and Unitary Transformations 194
6. Orthogonal and Unitary Matrices 195
7. Superdiagonal Form 199
8. Normal Matrices 201
9. Normal Linear Transformations 203
10. Hermitian and Unitary Matrices 208
11. Real Vector Spaces 209
12. The Computational Processes 213
VI Selected applications of linear algebra 219
1. Vector Geometry 220
2. Finite Cones and Linear Inequalities 229
3. Linear Programming 239
4. Applications to Communication Theory 253
5. Vector Calculus 259
6. Spectral Decomposition of Linear Transformations 270
7. Systems of Linear Differential Equations 278
8. Small Oscillations of Mechanical Systems 284
9. Representations of Finite Groups by Matrices 292
10. Application of Representation Theory to Symmetric Mechanical
Systems 312
Appendix 319
Answers to selected exercises 325
Index 345 |
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| index_date | 2024-07-02T16:05:27Z |
| indexdate | 2024-07-09T20:47:18Z |
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| language | English |
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| physical | XII, 352 S. |
| publishDate | 1970 |
| publishDateSearch | 1970 |
| publishDateSort | 1970 |
| publisher | Wiley |
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| spelling | Nering, Evar D. Verfasser aut Linear algebra and matrix theory Evar D. Nering 2. ed. New York [u.a.] Wiley 1970 XII, 352 S. txt rdacontent n rdamedia nc rdacarrier Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Matrizenrechnung (DE-588)4126963-9 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Matrizentheorie (DE-588)4128970-5 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s DE-604 Matrizenrechnung (DE-588)4126963-9 s Matrix Mathematik (DE-588)4037968-1 s 1\p DE-604 Matrizentheorie (DE-588)4128970-5 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015130422&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nering, Evar D. Linear algebra and matrix theory Matrix Mathematik (DE-588)4037968-1 gnd Matrizenrechnung (DE-588)4126963-9 gnd Lineare Algebra (DE-588)4035811-2 gnd Matrizentheorie (DE-588)4128970-5 gnd |
| subject_GND | (DE-588)4037968-1 (DE-588)4126963-9 (DE-588)4035811-2 (DE-588)4128970-5 |
| title | Linear algebra and matrix theory |
| title_auth | Linear algebra and matrix theory |
| title_exact_search | Linear algebra and matrix theory |
| title_exact_search_txtP | Linear algebra and matrix theory |
| title_full | Linear algebra and matrix theory Evar D. Nering |
| title_fullStr | Linear algebra and matrix theory Evar D. Nering |
| title_full_unstemmed | Linear algebra and matrix theory Evar D. Nering |
| title_short | Linear algebra and matrix theory |
| title_sort | linear algebra and matrix theory |
| topic | Matrix Mathematik (DE-588)4037968-1 gnd Matrizenrechnung (DE-588)4126963-9 gnd Lineare Algebra (DE-588)4035811-2 gnd Matrizentheorie (DE-588)4128970-5 gnd |
| topic_facet | Matrix Mathematik Matrizenrechnung Lineare Algebra Matrizentheorie |
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