Algebraic and computational aspects of real tensor ranks:
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| Main Authors: | , , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Tokyo
Springer
[2016]
|
| Series: | SpringerBriefs in statistics JSS research series in statistics
|
| Subjects: | |
| Online Access: | BTU01 FHR01 FRO01 TUM01 UBM01 UBT01 UBW01 UEI01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Physical Description: | 1 Online-Ressource (VIII, 108 Seiten, 5 illus) |
| ISBN: | 9784431554592 |
| ISSN: | 2191-544X |
| DOI: | 10.1007/978-4-431-55459-2 |
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Record in the Search Index
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| adam_text | ALGEBRAIC AND COMPUTATIONAL ASPECTS OF REAL TENSOR RANKS
/ SAKATA, TOSHIO
: 2016
TABLE OF CONTENTS / INHALTSVERZEICHNIS
BASICS OF TENSOR RANK
3-TENSORS
SIMPLE EVALUATION METHODS OF TENSOR RANK
ABSOLUTELY NONSINGULAR TENSORS AND DETERMINANTAL POLYNOMIALS
MAXIMAL RANKS
TYPICAL RANKS
GLOBAL THEORY OF TENSOR RANKS
2 × 2 × × 2 TENSORS
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
ALGEBRAIC AND COMPUTATIONAL ASPECTS OF REAL TENSOR RANKS
/ SAKATA, TOSHIO
: 2016
ABSTRACT / INHALTSTEXT
THIS BOOK PROVIDES COMPREHENSIVE SUMMARIES OF THEORETICAL (ALGEBRAIC)
AND COMPUTATIONAL ASPECTS OF TENSOR RANKS, MAXIMAL RANKS, AND TYPICAL
RANKS, OVER THE REAL NUMBER FIELD. ALTHOUGH TENSOR RANKS HAVE BEEN OFTEN
ARGUED IN THE COMPLEX NUMBER FIELD, IT SHOULD BE EMPHASIZED THAT THIS
BOOK TREATS REAL TENSOR RANKS, WHICH HAVE DIRECT APPLICATIONS IN
STATISTICS. THE BOOK PROVIDES SEVERAL INTERESTING IDEAS, INCLUDING
DETERMINANT POLYNOMIALS, DETERMINANTAL IDEALS, ABSOLUTELY NONSINGULAR
TENSORS, ABSOLUTELY FULL COLUMN RANK TENSORS, AND THEIR CONNECTION TO
BILINEAR MAPS AND HURWITZ-RADON NUMBERS. IN ADDITION TO REVIEWS OF
METHODS TO DETERMINE REAL TENSOR RANKS IN DETAILS, GLOBAL THEORIES SUCH
AS THE JACOBIAN METHOD ARE ALSO REVIEWED IN DETAILS. THE BOOK INCLUDES
AS WELL AN ACCESSIBLE AND COMPREHENSIVE INTRODUCTION OF MATHEMATICAL
BACKGROUNDS, WITH BASICS OF POSITIVE POLYNOMIALS AND CALCULATIONS BY
USING THE GROEBNER BASIS. FURTHERMORE, THIS BOOK PROVIDES INSIGHTS INTO
NUMERICAL METHODS OF FINDING TENSOR RANKS THROUGH SIMULTANEOUS SINGULAR
VALUE DECOMPOSITIONS
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Sakata, Toshio Sumi, Toshio Miyazaki, Mitsuhiro |
| author_GND | (DE-588)1084652668 (DE-588)1099463831 (DE-588)1099465230 |
| author_facet | Sakata, Toshio Sumi, Toshio Miyazaki, Mitsuhiro |
| author_role | aut aut aut |
| author_sort | Sakata, Toshio |
| author_variant | t s ts t s ts m m mm |
| building | Verbundindex |
| bvnumber | BV043503705 |
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| dewey-full | 519.5 |
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| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-4-431-55459-2 |
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| isbn | 9784431554592 |
| issn | 2191-544X |
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| spelling | Sakata, Toshio Verfasser (DE-588)1084652668 aut Algebraic and computational aspects of real tensor ranks Toshio Sakata, Toshio Sumi, Mitsuhiro Miyazaki Tokyo Springer [2016] © 2016 1 Online-Ressource (VIII, 108 Seiten, 5 illus) txt rdacontent c rdamedia cr rdacarrier SpringerBriefs in statistics JSS research series in statistics 2191-544X Statistics Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences Statistics and Computing/Statistics Programs Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law Statistik Sumi, Toshio Verfasser (DE-588)1099463831 aut Miyazaki, Mitsuhiro Verfasser (DE-588)1099465230 aut Erscheint auch als Druckausgabe 978-4-431-55458-5 https://doi.org/10.1007/978-4-431-55459-2 Verlag URL des Erstveröffentlichers Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028920050&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028920050&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Sakata, Toshio Sumi, Toshio Miyazaki, Mitsuhiro Algebraic and computational aspects of real tensor ranks Statistics Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences Statistics and Computing/Statistics Programs Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law Statistik |
| title | Algebraic and computational aspects of real tensor ranks |
| title_auth | Algebraic and computational aspects of real tensor ranks |
| title_exact_search | Algebraic and computational aspects of real tensor ranks |
| title_full | Algebraic and computational aspects of real tensor ranks Toshio Sakata, Toshio Sumi, Mitsuhiro Miyazaki |
| title_fullStr | Algebraic and computational aspects of real tensor ranks Toshio Sakata, Toshio Sumi, Mitsuhiro Miyazaki |
| title_full_unstemmed | Algebraic and computational aspects of real tensor ranks Toshio Sakata, Toshio Sumi, Mitsuhiro Miyazaki |
| title_short | Algebraic and computational aspects of real tensor ranks |
| title_sort | algebraic and computational aspects of real tensor ranks |
| topic | Statistics Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences Statistics and Computing/Statistics Programs Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law Statistik |
| topic_facet | Statistics Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences Statistics and Computing/Statistics Programs Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law Statistik |
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