Matrix theory: basic results and techniques
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2011
|
| Edition: | 2. ed. |
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 399 S. Ill., graph. Darst. |
| ISBN: | 9781461410980 9781461410997 |
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MARC
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Record in the Search Index
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|---|---|
| adam_text | Titel: Matrix theory
Autor: Zhang, Fuzhen
Jahr: 2011
Contents
Preface to the Second Edition ...................................vii
Preface..............................................................ix
Frequently Used Notation and Terminology....................xv
Frequently Used Theorems .....................................xvii
1 Elementary Linear Algebra Review 1
1.1 Vector Spaces ...............................................1
1.2 Matrices and Determinants ..................................8
1.3 Linear Transformations and Eigenvalues ....................17
1.4 Inner Product Spaces ......................................27
2 Partitioned Matrices, Rank, and Eigenvalues 35
2.1 Elementary Operations of Partitioned Matrices .............35
2.2 The Determinant and Inverse of Partitioned Matrices.......42
2.3 The Rank of Product and Sum .............................51
2.4 The Eigenvalues of AB and BA ............................57
2.5 The Continuity Argument and Matrix Functions ...........62
2.6 Localization of Eigenvalues: The Gersgorin Theorem .......67
3 Matrix Polynomials and Canonical Forms 73
3.1 Commuting Matrices .......................................73
3.2 Matrix Decompositions.....................................79
3.3 Annihilating Polynomials of Matrices.......................87
3.4 Jordan Canonical Forms ...................................93
3.5 The Matrices AT, A, A*, ATA, A*A, and AA ............102
4 Numerical Ranges, Matrix Norms, and Special Operations 107
4.1 Numerical Range and Radius .............................107
4.2 Matrix Norms.............................................113
4.3 The Kronecker and Hadamard Products...................117
4.4 Compound Matrices ......................................122
5 Special Types of Matrices 125
5.1 Idempotence, Nilpotence, Involution, and Projections......125
5.2 Tridiagonal Matrices ......................................133
5.3 Circulant Matrices ........................................138
5.4 Vandermonde Matrices ....................................143
5.5 Hadamard Matrices .......................................150
5.6 Permutation and Doubly Stochastic Matrices..............155
5.7 Nonnegative Matrices .....................................164
6 Unitary Matrices and Contractions 171
6.1 Properties of Unitary Matrices ............................171
6.2 Real Orthogonal Matrices .................................177
6.3 Metric Space and Contractions ............................182
6.4 Contractions and Unitary Matrices ........................188
6.5 The Unitary Similarity of Real Matrices...................192
6.6 A Trace Inequality of Unitary Matrices....................195
7 Positive Semidefinite Matrices 199
7.1 Positive Semidefinite Matrices.............................199
7.2 A Pair of Positive Semidefinite Matrices...................207
7.3 Partitioned Positive Semidefinite Matrices .................217
7.4 Schur Complements and Determinant Inequalities .........227
7.5 The Kronecker and Hadamard Products
of Positive Semidefinite Matrices ..........................234
7.6 Schur Complements and the Hadamard Product...........240
7.7 The Wielandt and Kantorovich Inequalities ...............245
8 Hermitian Matrices 253
8.1 Hermitian Matrices and Their Inertias ....................253
8.2 The Product of Hermitian Matrices .......................260
8.3 The Min-Max Theorem and Interlacing Theorem ..........266
8.4 Eigenvalue and Singular Value Inequalities ................274
8.5 Eigenvalues of Hermitian matrices A, B, and A + B .......281
8.6 A Triangle Inequality for the Matrix {A* Aft2 ............287
9 Normal Matrices 293
9.1 Equivalent Conditions.....................................293
9.2 Normal Matrices with Zero and One Entries...............306
9.3 Normality and Cauchy-Schwarz-Type Inequality ..........312
9.4 Normal Matrix Perturbation ..............................319
10 Majorization and Matrix Inequalities 325
10.1 Basic Properties of Majorization ........................325
10.2 Majorization and Stochastic Matrices ...................334
10.3 Majorization and Convex Functions.....................340
10.4 Majorization of Diagonal Entries, Eigenvalues,
and Singular Values ....................................349
10.5 Majorization for Matrix Sum ...........................356
10.6 Majorization for Matrix Product ........................363
10.7 Majorization and Unitarily Invariant Norms ............372
References .........................................................379
Notation ..........................................................391
Index ..............................................................395
|
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| dewey-full | 512.9/434 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/434 |
| dewey-search | 512.9/434 |
| dewey-sort | 3512.9 3434 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T23:59:57Z |
| institution | BVB |
| isbn | 9781461410980 9781461410997 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024163437 |
| oclc_num | 745514674 |
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| physical | XVII, 399 S. Ill., graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
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| series2 | Universitext |
| spelling | Zhang, Fuzhen 1961- Verfasser (DE-588)121250008 aut Matrix theory basic results and techniques Fuzhen Zhang 2. ed. New York [u.a.] Springer 2011 XVII, 399 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Matrizentheorie Matrices Matrizentheorie (DE-588)4128970-5 gnd rswk-swf Matrizentheorie (DE-588)4128970-5 s DE-604 Erscheint auch als Online-Ausgabe 10.1007/978-1-4614-1099-7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024163437&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zhang, Fuzhen 1961- Matrix theory basic results and techniques Matrizentheorie Matrices Matrizentheorie (DE-588)4128970-5 gnd |
| subject_GND | (DE-588)4128970-5 |
| title | Matrix theory basic results and techniques |
| title_auth | Matrix theory basic results and techniques |
| title_exact_search | Matrix theory basic results and techniques |
| title_full | Matrix theory basic results and techniques Fuzhen Zhang |
| title_fullStr | Matrix theory basic results and techniques Fuzhen Zhang |
| title_full_unstemmed | Matrix theory basic results and techniques Fuzhen Zhang |
| title_short | Matrix theory |
| title_sort | matrix theory basic results and techniques |
| title_sub | basic results and techniques |
| topic | Matrizentheorie Matrices Matrizentheorie (DE-588)4128970-5 gnd |
| topic_facet | Matrizentheorie Matrices |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024163437&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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