Bilinear forms and zonal polynomials:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Springer
1995
|
| Series: | Lecture notes in statistics
102 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 376 S. |
| ISBN: | 0387945229 |
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MARC
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| 100 | 1 | |a Mathai, Arakaparampil M. |d 1935- |e Verfasser |0 (DE-588)141316241 |4 aut | |
| 245 | 1 | 0 | |a Bilinear forms and zonal polynomials |c A. M. Mathai, Serge B. Provost, and Takesi Hayakawa |
| 264 | 1 | |a New York u.a. |b Springer |c 1995 | |
| 300 | |a XII, 376 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in statistics |v 102 | |
| 650 | 4 | |a Formes bilinéaires | |
| 650 | 7 | |a Multilineaire vormen |2 gtt | |
| 650 | 7 | |a Polynomen |2 gtt | |
| 650 | 4 | |a Polynômes zonaux | |
| 650 | 7 | |a Polynômes zonaux |2 ram | |
| 650 | 4 | |a Bilinear forms | |
| 650 | 4 | |a Zonal polynomials | |
| 650 | 0 | 7 | |a Bilinearform |0 (DE-588)4138018-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zonales Polynom |0 (DE-588)4386588-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zufallsvektor |0 (DE-588)4191098-9 |2 gnd |9 rswk-swf |
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| 689 | 1 | 0 | |a Zonales Polynom |0 (DE-588)4386588-4 |D s |
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| 700 | 1 | |a Provost, Serge B. |e Verfasser |4 aut | |
| 700 | 1 | |a Hayakawa, Takesi |d 1940- |e Verfasser |0 (DE-588)11371503X |4 aut | |
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Record in the Search Index
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|---|---|
| adam_text | A.M. MATHAI, SERGE B. PROVOST, AND TAKESI HAYAKAWA BILINEAR FORMS AND
ZONAL POLYNOMIALS SPRINGER-VERLAG NEW YORK BERLIN HEIDELBERG LONDON
PARIS TOKYO HONGKONG BARCELONA BUDAPEST CONTENTS PREFACE VII CHAPTER 1
PRELIMINARIES 1.0 INTRODUCTION 1 1.1 JACOBIANS OF MATRIX TRANSFORMATIONS
1 1.1A SOME FREQUENTLY USED JACOBIANS IN THE REAL CASE 2 1.2 SINGULAR
AND NONSINGULAR NORMAL DISTRIBUTIONS 6 1.2A NORMAL DISTRIBUTION IN THE
REAL CASE 6 1.2B THE MOMENT GENERATING FUNCTION FOR THE REAL NORMAL
DISTRIBUTION 7 1.3 QUADRATIC FORMS IN NORMAL VARIABLES 8 1.3A
REPRESENTATIONS OF A QUADRATIC FORM 8 1.3B REPRESENTATIONS OF THE M.G.F.
OF A QUADRATIC EXPRESSION 9 1.4 MATRIX-VARIATE GAMMA AND BETA FUNCTIONS
10 1.4A MATRIX-VARIATE GAMMA, REAI CASE 10 1.4B MATRIX-VARIATE GAMMA
DENSITY, REAL CASE 12 1.4C THE M.G.F. OF A MATRIX-VARIATE REAL GAMMA
VARIABLE 13 1.4D MATRIX-VARIATE BETA, REAI CASE 13 1.5 HYPERGEOMETRIC
SERIES, REAL CASE 16 CHAPTER 2 QUADRATIC AND BILINEAR FORMS IN NORMAL
VECTORS 2.0 INTRODUCTION 17 2.1 VARIOUS REPRESENTATIONS 19 2.2 DENSITY
OF A GAMMA DIFFERENCE 20 2.2A SOME PARTICULAR CASES 22 2.3 NONCENTRAL
GAMMA DIFFERENCE 24 2.4 MOMENTS AND CUMULANTS OF BILINEAR FORMS 27 2.4A
JOINT MOMENTS AND CUMULANTS OF QUADRATIC AND BILINEAR FORMS 28 IX X
CONTENTS 2.4A. 1 THE FIRST FEW JOINT CUMULANTS OF A BILINEAR FORM AND A
QUADRATIC FORM IN THE NONSINGULAR NORMAL CASE 31 2.4A.2 THE FIRST FEW
CUMULANTS OF A QUADRATIC FORM IN THE NONSINGULAR NORMAL CASE . . . .
33 2.4A.3 THE FIRST FEW CUMULANTS OF A BILINEAR FORM IN THE NONSINGULAR
NORMAL CASE 34 2.4B JOINT CUMULANTS OF BILINEAR FORMS 35 2.4B. 1 THE
FIRST FEW JOINT CUMULANTS OF OF TWO BILINEAR FORMS 37 2.4C MOMENTS AND
CUMULANTS IN THE SINGULAR NORMAL CASE 39 2.4C. 1 THE FIRST FEW CUMULANTS
OF A BILINEAR FORM IN THE SINGULAR AND NONSINGULAR NORMAL CASES 40 2.4D
CUMULANTS OF BILINEAR EXPRESSIONS 42 2.4D.L SOME SPECIAL CASES OF
BILINEAR EXPRESSIONS 42 2.5 LAPLACIANNESS OF BILINEAR FORMS 45 2.5A
QUADRATIC AND BILINEAR FORMS IN THE NONSINGULAR NORMAL CASE 47 2.5B NS
CONDITIONS FOR THE NONCORRELATED NORMAL CASE 50 2.5C QUADRATIC AND
BILINEAR FORMS IN THE SINGULAR NORMAL CASE 52 2.5D NONCORRELATED
SINGULAR NORMAL CASE 54 2.5E THE NS CONDITIONS FOR A QUADRATIC FORM TO
BE NGL 55 2.6 GENERALIZATIONS TO BILINEAR AND QUADRATIC EXPRESSIONS 57
2.6A BILINEAR AND QUADRATIC EXPRESSIONS IN THE NONSINGULAR NORMAL CASE
57 2.6B BILINEAR AND QUADRATIC EXPRESSIONS IN THE SINGULAR NORMAL CASE
61 2.7 INDEPENDENCE OF BILINEAR AND QUADRATIC EXPRESSIONS 63 2.7A
INDEPENDENCE OF A BILINEAR AND A QUADRATIC FORM 63 2.7B INDEPENDENCE OF
TWO BILINEAR FORMS 65 2.7C INDEPENDENCE OF QUADRATIC EXPRESSIONS:
NONSINGULAR NORMAL CASE 67 2.7D INDEPENDENCE IN THE SINGULAR NORMAL CASE
70 2.8 BILINEAR FORMS AND NONCENTRAL GAMMA DIFFERENCES 74 2.8A BILINEAR
FORMS IN THE EQUICORRELATED CASE 75 2.8B NONCENTRAL CASE 78 2.9
RECTANGULAR MATRICES 80 2.9A MATRIX-VARIATE LAPLACIAN 82 2.9B THE
DENSITY OF SU 83 2.9C A PARTICULAR CASE 84 EXERCISES 86 CONTENTS XI
CHAPTER 3 QUADRATIC AND BILINEAR FORMS IN ELLIPTICALLY CONTOURED
DISTRIBUTIONS 3.0 INTRODUCTION 89 3.1 DESSNITIONS AND BASIC RESULTS 91
3.2 MOMENTS OF QUADRATIC FORMS 104 3.3 THE DISTRIBUTION OF QUADRATIC
FORMS 111 3.4 NONCENTRAL DISTRIBUTION 116 3.5 QUADRATIC FORMS IN RANDOM
MATRICES 122 3.6 QUADRATIC FORMS OF RANDOM IDEMPOTENT MATRICES 123 3.7
COCHRAN S THEOREM 131 3.8 TEST STATISTICS FOR ELLIPTICALLY CONTOURED
DISTRIBUTIONS 138 SAMPLE CORRELATION COEFRCIENT 139 LIKELIHOOD RATIO
CRITERIA 145 EXERCISES 155 CHAPTER 4 ZONAL POLYNOMIALS 4.0 INTRODUCTION
163 4.1 WI SHART DISTRIBUTION 163 4.2 SYMMETRIE POLYNOMIALS 166 4.3
ZONAL POLYNOMIALS 171 4.4 LAPLACE TRANSFORM AND HYPERGEOMETRIC FUNCTION
193 4.5 BINOMIAL COEFFICIENTS 210 4.6 SOME SPECIAL FUNCTIONS 215
EXERCISES 234 TABLE 4.3.2(A) 243 TABLE 4.3.2(B) 244 TABLE 4.4.1 246
CHAPTER 5 GENERALIZED QUADRATIC FORMS 5.0 INTRODUCTION 247 5.1 A
REPRESENTATION OF THE DISTRIBUTION OF A GENERALIZED QUADRATIC FORM 248
5.2 AN ALTERNATE REPRESENTATION 255 5.3 THE DISTRIBUTION OF THE LATENT
ROOTS OF A QUADRATIC FORM 258 5.4 DISTRIBUTIONS OF SOME FUNCTIONS OF
XAX 264 5.5 GENERALIZED HOTELLING S T 02 268 5.6 ANDERSON S LINEAR
DISCRIMINANT FUNCTION 279 5.7 MUITIVARIATE CALIBRATION 286 5.8
ASYMPTOTIC EXPANSIONS OF THE DISTRIBUTION OF A QUADRATIC FORM 294
EXERCISES 300 XII CONTENTS TABLE 5.6.1 317 TABLE 5.6.2 318 APPENDIX
INVARIANT POLYNOMIALS APPENDIX A.L REPRESENTATION OF A GROUP 319
APPENDIX A.2 INTEGRATION OF THE REPRESENTATION MATRIX OVER THE
ORTHOGONAL GROUP 323 APPENDIX A.3 RINDAMENTAL PROPERTIES OF C X (X, Y)
325 BIBLIOGRAPHY 353 GLOSSARY OF SYMBOLS 363 AUTHOR INDEX 371 SUBJECT
INDEX 375
|
| any_adam_object | 1 |
| author | Mathai, Arakaparampil M. 1935- Provost, Serge B. Hayakawa, Takesi 1940- |
| author_GND | (DE-588)141316241 (DE-588)11371503X |
| author_facet | Mathai, Arakaparampil M. 1935- Provost, Serge B. Hayakawa, Takesi 1940- |
| author_role | aut aut aut |
| author_sort | Mathai, Arakaparampil M. 1935- |
| author_variant | a m m am amm s b p sb sbp t h th |
| building | Verbundindex |
| bvnumber | BV010317721 |
| callnumber-first | Q - Science |
| callnumber-label | QA243 |
| callnumber-raw | QA243.M26 1995 |
| callnumber-search | QA243.M26 1995 |
| callnumber-sort | QA 3243 M26 41995 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 856 SK 820 |
| ctrlnum | (OCoLC)32550217 (DE-599)BVBBV010317721 |
| dewey-full | 512.9/4420 512.9/44 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/44 20 512.9/44 |
| dewey-search | 512.9/44 20 512.9/44 |
| dewey-sort | 3512.9 244 220 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010317721 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:50:25Z |
| institution | BVB |
| isbn | 0387945229 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006865654 |
| oclc_num | 32550217 |
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| owner_facet | DE-739 DE-824 DE-12 DE-19 DE-BY-UBM DE-703 DE-384 DE-706 DE-521 DE-634 DE-83 DE-11 |
| physical | XII, 376 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in statistics |
| series2 | Lecture notes in statistics |
| spelling | Mathai, Arakaparampil M. 1935- Verfasser (DE-588)141316241 aut Bilinear forms and zonal polynomials A. M. Mathai, Serge B. Provost, and Takesi Hayakawa New York u.a. Springer 1995 XII, 376 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in statistics 102 Formes bilinéaires Multilineaire vormen gtt Polynomen gtt Polynômes zonaux Polynômes zonaux ram Bilinear forms Zonal polynomials Bilinearform (DE-588)4138018-6 gnd rswk-swf Zonales Polynom (DE-588)4386588-4 gnd rswk-swf Zufallsvektor (DE-588)4191098-9 gnd rswk-swf Bilinearform (DE-588)4138018-6 s Zufallsvektor (DE-588)4191098-9 s DE-604 Zonales Polynom (DE-588)4386588-4 s Provost, Serge B. Verfasser aut Hayakawa, Takesi 1940- Verfasser (DE-588)11371503X aut Lecture notes in statistics 102 (DE-604)BV002447846 102 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006865654&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mathai, Arakaparampil M. 1935- Provost, Serge B. Hayakawa, Takesi 1940- Bilinear forms and zonal polynomials Lecture notes in statistics Formes bilinéaires Multilineaire vormen gtt Polynomen gtt Polynômes zonaux Polynômes zonaux ram Bilinear forms Zonal polynomials Bilinearform (DE-588)4138018-6 gnd Zonales Polynom (DE-588)4386588-4 gnd Zufallsvektor (DE-588)4191098-9 gnd |
| subject_GND | (DE-588)4138018-6 (DE-588)4386588-4 (DE-588)4191098-9 |
| title | Bilinear forms and zonal polynomials |
| title_auth | Bilinear forms and zonal polynomials |
| title_exact_search | Bilinear forms and zonal polynomials |
| title_full | Bilinear forms and zonal polynomials A. M. Mathai, Serge B. Provost, and Takesi Hayakawa |
| title_fullStr | Bilinear forms and zonal polynomials A. M. Mathai, Serge B. Provost, and Takesi Hayakawa |
| title_full_unstemmed | Bilinear forms and zonal polynomials A. M. Mathai, Serge B. Provost, and Takesi Hayakawa |
| title_short | Bilinear forms and zonal polynomials |
| title_sort | bilinear forms and zonal polynomials |
| topic | Formes bilinéaires Multilineaire vormen gtt Polynomen gtt Polynômes zonaux Polynômes zonaux ram Bilinear forms Zonal polynomials Bilinearform (DE-588)4138018-6 gnd Zonales Polynom (DE-588)4386588-4 gnd Zufallsvektor (DE-588)4191098-9 gnd |
| topic_facet | Formes bilinéaires Multilineaire vormen Polynomen Polynômes zonaux Bilinear forms Zonal polynomials Bilinearform Zonales Polynom Zufallsvektor |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006865654&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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