Geometry of matrices: in memory of Professor L. K. Hua (1910 - 1985)
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
1996
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 376 S. |
| ISBN: | 9810226381 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Preface v
1 Linear Algebra over Division Rings 1
1.1 Vector Spaces over Division Rings 1
1.2 Matrices over Division Rings 11
1.3 Matrix Representations of Subspaces 27
1.4 Systems of Linear Equations 29
1.5 Hermitian, Symmetric, and Alternate Matrices 35
1.6 Comments 44
2 Affine Geometry and Projective Geometry 45
2.1 Affine Spaces and Affine Groups 45
2.2 Fundamental Theorem of the Affine Geometry 54
2.3 Projective Spaces and Projective Groups 66
2.4 Fundamental Theorem of the Projective Geometry 76
2.5 One dimensional Projective Geometry 80
2.6 Comments 87
3 Geometry of Rectangular Matrices 89
3.1 The Space of Rectangular Matrices 89
3.2 Maximal Sets of Rank 1 93
3.3 Maximal Sets of Rank 2 97
3.4 Proof of the Fundamental Theorem 106
3.5 Application to Algebra 118
3.6 Application to Geometry 123
3.7 Application to Geometry (Continued) 139
vii
viii CONTENTS
3.8 Application to Graph Theory 153
3.9 Comments 155
4 Geometry of Alternate Matrices 157
4.1 The Space of Alternate Matrices 157
4.2 Maximal Sets 159
4.3 Proof of the Fundamental Theorem 168
4.4 Application to Geometry 177
4.5 Application to Geometry (Continued) 199
4.6 Application to Graph Theory 211
4.7 Comments 215
5 Geometry of Symmetric Matrices 217
5.1 The Space of Symmetric Matrices 217
5.2 Maximal Sets of Rank 1 222
5.3 Maximal Sets of Rank 2 (Characteristic Not Two) 224
5.4 Proof of the Fundamental Theorem (I) 231
5.5 Maximal Sets of Rank 2 (Characteristic Two) 244
5.6 Proof of the Fundamental Theorem (II) 252
5.7 Proof of the Fundamental Theorem (III) 264
5.8 Application to Algebra 281
5.9 Application to Geometry 285
5.10 Application to Graph Theory 296
5.11 Comments 303
6 Geometry of Hermitian Matrices 305
6.1 The Space of Hermitian Matrices 305
6.2 Maximal Sets of Rank 1 308
6.3 Maximal Sets of Rank 2 311
6.4 Proof of the Fundamental Theorem (the Case n 3) .... 323
6.5 Maximal Sets of Rank 2 (the Case n = 2) 341
6.6 Proof of the Fundamental Theorem (the Case n = 2) .... 348
6.7 Application to Algebra 355
6.8 Application to Geometry 356
6.9 Application to Graph Theory 363
CONTENTS ix
6.10 Comments 365
Bibliography 367
Index 371
|
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| isbn | 9810226381 |
| language | English |
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| physical | IX, 376 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
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| publisher | World Scientific |
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| spelling | Wan, Zhexian 1927- Verfasser (DE-588)132646943 aut Geometry of matrices in memory of Professor L. K. Hua (1910 - 1985) Zhe-Xian Wan Singapore [u.a.] World Scientific 1996 IX, 376 S. txt rdacontent n rdamedia nc rdacarrier Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf (DE-588)4016928-5 Festschrift gnd-content Matrix Mathematik (DE-588)4037968-1 s Geometrie (DE-588)4020236-7 s DE-604 Hua, L. K. hnr HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007385278&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wan, Zhexian 1927- Geometry of matrices in memory of Professor L. K. Hua (1910 - 1985) Matrix Mathematik (DE-588)4037968-1 gnd Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4037968-1 (DE-588)4020236-7 (DE-588)4016928-5 |
| title | Geometry of matrices in memory of Professor L. K. Hua (1910 - 1985) |
| title_auth | Geometry of matrices in memory of Professor L. K. Hua (1910 - 1985) |
| title_exact_search | Geometry of matrices in memory of Professor L. K. Hua (1910 - 1985) |
| title_full | Geometry of matrices in memory of Professor L. K. Hua (1910 - 1985) Zhe-Xian Wan |
| title_fullStr | Geometry of matrices in memory of Professor L. K. Hua (1910 - 1985) Zhe-Xian Wan |
| title_full_unstemmed | Geometry of matrices in memory of Professor L. K. Hua (1910 - 1985) Zhe-Xian Wan |
| title_short | Geometry of matrices |
| title_sort | geometry of matrices in memory of professor l k hua 1910 1985 |
| title_sub | in memory of Professor L. K. Hua (1910 - 1985) |
| topic | Matrix Mathematik (DE-588)4037968-1 gnd Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Matrix Mathematik Geometrie Festschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007385278&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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