Matrix theory and applications for engineers and mathematicians:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester
Horwood
1979
|
| Series: | Mathematics and its applications.
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 295 S. graph. Darst. |
| ISBN: | 085312129X |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804116635810791424 |
|---|---|
| adam_text | Table of Contents
Preface 7
Chapter 1 — Matrices
1.1 Matrices and Matrix Operations 9
1.2 Some Properties of Matrix Operations 17
1.3 Partitioned Matrices 26
1.4 Some Special Matrices 28
1.5 The State Space Concept 33
Chapter 2 Vector Spaces
2.1 Vectors 43
2.2 Linear Dependence and Bases 51
2.3 Coordinates and the Transition Matrix 59
Chapter 3 — Linear Transformations
3.1 Homomorphisms 69
3.2 Isomorphism and Vector Spaces 74
3.3 Linear Transformations and Matrices 77
3.4 Orthogonal Transformations 86
3.5 General Change of Bases for a Linear Transformation 89
Chapter 4 The Rank and the Determinant of a Matrix
4.1 The Kernel and the Image Space of a Linear Transformation 97
4.2 The Rank of a Matrix 103
4.3 The Determinant of a Matrix 113
4.4 Operations with Determinants 118
4.5 Cramer s Rule 120
Chapter 5 — Linear Equations
5.1 Systems of Homogeneous Equations 131
5.2 Systems of Non Homogeneous Equations 136
6 Table of Contents
Chapter 6 — Eigenvectors and Eigenvalues
6.1 The Characteristic Equation 144
6.2 The Eigenvalues of the transposed matrix 149
6.3 When all the Eigenvalues of A are distinct 152
6.4 A reduction to a Diagonal Form 155
6.5 Multiple Eigenvalues 160
6.6 The Cayley Hamilton Theorem 165
Chapter 7 — Canonical Forms and Matrix Functions
7.1 Polynomials 177
7.2 Eigenvalues of Rational Functions of a Matrix 179
7.3 The Minimum Polynomial of a Matrix 185
7.4 Direct Sums and Invariant Subspaces 187
7.5 A Decomposition of a Vector Space 197
7.6 Cyclic Bases and the Rational Canonical Form 205
7.7 The Jordan Canonical Forms 217
7.8 Matrix Functions 224
Chapter 8 — Inverting a Matrix
8.1 Elementary Operations and Elementrry Matrices 238
8.2 The Inverse of a Vandermonde Matrix 245
8.3 Faddeeva s Method 250
8.4 Inverting a Matrix with Complex Elements 255
Solutions to Problems 263
References and Bibliography 291
Index 293
|
| any_adam_object | 1 |
| author | Graham, Alexander |
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| callnumber-first | Q - Science |
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| callnumber-raw | QA188 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 220 |
| ctrlnum | (OCoLC)5336786 (DE-599)BVBBV002180228 |
| dewey-full | 512.9/43 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/43 |
| dewey-search | 512.9/43 |
| dewey-sort | 3512.9 243 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002180228 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:41:39Z |
| institution | BVB |
| isbn | 085312129X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001431978 |
| oclc_num | 5336786 |
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| owner_facet | DE-91G DE-BY-TUM DE-384 DE-473 DE-BY-UBG DE-739 DE-188 |
| physical | 295 S. graph. Darst. |
| publishDate | 1979 |
| publishDateSearch | 1979 |
| publishDateSort | 1979 |
| publisher | Horwood |
| record_format | marc |
| series2 | Mathematics and its applications. |
| spelling | Graham, Alexander Verfasser aut Matrix theory and applications for engineers and mathematicians Chichester Horwood 1979 295 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications. Algèbre linéaire Matrices Algebras, Linear Matrizentheorie (DE-588)4128970-5 gnd rswk-swf Matrizenrechnung (DE-588)4126963-9 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Matrizenrechnung (DE-588)4126963-9 s DE-604 Lineare Algebra (DE-588)4035811-2 s Matrizentheorie (DE-588)4128970-5 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001431978&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 |
| spellingShingle | Graham, Alexander Matrix theory and applications for engineers and mathematicians Algèbre linéaire Matrices Algebras, Linear Matrizentheorie (DE-588)4128970-5 gnd Matrizenrechnung (DE-588)4126963-9 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4128970-5 (DE-588)4126963-9 (DE-588)4035811-2 |
| title | Matrix theory and applications for engineers and mathematicians |
| title_auth | Matrix theory and applications for engineers and mathematicians |
| title_exact_search | Matrix theory and applications for engineers and mathematicians |
| title_full | Matrix theory and applications for engineers and mathematicians |
| title_fullStr | Matrix theory and applications for engineers and mathematicians |
| title_full_unstemmed | Matrix theory and applications for engineers and mathematicians |
| title_short | Matrix theory and applications for engineers and mathematicians |
| title_sort | matrix theory and applications for engineers and mathematicians |
| topic | Algèbre linéaire Matrices Algebras, Linear Matrizentheorie (DE-588)4128970-5 gnd Matrizenrechnung (DE-588)4126963-9 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Algèbre linéaire Matrices Algebras, Linear Matrizentheorie Matrizenrechnung Lineare Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001431978&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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