When does cp-rank equal rank?

Name: Work Video:
Duration: 3 min 30 s
Description: The problem of finding completely positive matrices with equal cp-rank and rank is considered. We give some easy-to-check sufficient conditions on the entries of a doubly nonnegative matrix for it to be completely positive with equal cp-rank and rank. An algorithm is also presented to show its efficiency.
Wasin So; Changqing Xu
{'id': 'https://openalex.org/W2152992791', 'doi': 'https://doi.org/10.48550/arxiv.1308.3193', 'title': 'When does cp-rank equal rank?', 'display_name': 'When does cp-rank equal rank?', 'publication_year': 2013, 'publication_date': '2013-01-01', 'ids': {'openalex': 'https://openalex.org/W2152992791', 'doi': 'https://doi.org/10.48550/arxiv.1308.3193', 'mag': '2152992791'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1308.3193', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'type': 'preprint', 'type_crossref': 'posted-content', 'indexed_in': ['datacite'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'https://arxiv.org/abs/1308.3193', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5070481718', 'display_name': 'Wasin So', 'orcid': None}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Wasin So', 'raw_affiliation_strings': [], 'affiliations': []}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5019220686', 'display_name': 'Changqing Xu', 'orcid': 'https://orcid.org/0000-0002-3774-1369'}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Changqing Xu', 'raw_affiliation_strings': [], 'affiliations': []}], 'institution_assertions': [], 'countries_distinct_count': 0, 'institutions_distinct_count': 0, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': None, 'has_fulltext': False, 'cited_by_count': 1, 'citation_normalized_percentile': {'value': 0.428571, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 65, 'max': 72}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T12303', 'display_name': 'Tensor decomposition and applications', 'score': 0.9981, 'subfield': {'id': 'https://openalex.org/subfields/2605', 'display_name': 'Computational Mathematics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T12303', 'display_name': 'Tensor decomposition and applications', 'score': 0.9981, 'subfield': {'id': 'https://openalex.org/subfields/2605', 'display_name': 'Computational Mathematics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T10792', 'display_name': 'Matrix Theory and Algorithms', 'score': 0.9875, 'subfield': {'id': 'https://openalex.org/subfields/1703', 'display_name': 'Computational Theory and Mathematics'}, 'field': {'id': 'https://openalex.org/fields/17', 'display_name': 'Computer Science'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T10963', 'display_name': 'Advanced Optimization Algorithms Research', 'score': 0.978, 'subfield': {'id': 'https://openalex.org/subfields/2612', 'display_name': 'Numerical Analysis'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/rank', 'display_name': 'Rank (graph theory)', 'score': 0.85382026}], 'concepts': [{'id': 'https://openalex.org/C164226766', 'wikidata': 'https://www.wikidata.org/wiki/Q7293202', 'display_name': 'Rank (graph theory)', 'level': 2, 'score': 0.85382026}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.58500254}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.38348392}, {'id': 'https://openalex.org/C105795698', 'wikidata': 'https://www.wikidata.org/wiki/Q12483', 'display_name': 'Statistics', 'level': 1, 'score': 0.34757823}], 'mesh': [], 'locations_count': 2, 'locations': [{'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1308.3193', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': False, 'landing_page_url': 'https://api.datacite.org/dois/10.48550/arxiv.1308.3193', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4393179698', 'display_name': 'DataCite API', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I4210145204', 'host_organization_name': 'DataCite', 'host_organization_lineage': ['https://openalex.org/I4210145204'], 'host_organization_lineage_names': ['DataCite'], 'type': 'metadata'}, 'license': None, 'license_id': None, 'version': None}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1308.3193', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 9, 'referenced_works': ['https://openalex.org/W1969807530', 'https://openalex.org/W1976335834', 'https://openalex.org/W2026654387', 'https://openalex.org/W2052505878', 'https://openalex.org/W2103339967', 'https://openalex.org/W2144920235', 'https://openalex.org/W2168446235', 'https://openalex.org/W2169053534', 'https://openalex.org/W828079620'], 'related_works': ['https://openalex.org/W4391375266', 'https://openalex.org/W4238204885', 'https://openalex.org/W3002753104', 'https://openalex.org/W2600246793', 'https://openalex.org/W2142036596', 'https://openalex.org/W2077600819', 'https://openalex.org/W2072657027', 'https://openalex.org/W2061531152', 'https://openalex.org/W2007980826', 'https://openalex.org/W1979597421'], 'abstract_inverted_index': {'The': [0], 'problem': [1], 'of': [2, 23], 'finding': [3], 'completely': [4, 32], 'positive': [5, 33], 'matrices': [6], 'with': [7, 34], 'equal': [8, 35], 'cp-rank': [9, 36], 'and': [10, 37], 'rank': [11], 'is': [12, 41], 'considered.': [13], 'We': [14], 'give': [15], 'some': [16], 'easy-to-check': [17], 'sufficient': [18], 'conditions': [19], 'on': [20], 'the': [21], 'entries': [22], 'a': [24], 'doubly': [25], 'nonnegative': [26], 'matrix': [27], 'for': [28], 'it': [29], 'to': [30, 44], 'be': [31], 'rank.': [38], 'An': [39], 'algorithm': [40], 'also': [42], 'presented': [43], 'show': [45], 'its': [46], 'efficiency.': [47]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2152992791', 'counts_by_year': [{'year': 2017, 'cited_by_count': 1}], 'updated_date': '2024-12-17T08:00:27.429410', 'created_date': '2016-06-24'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
