{"id":"https://openalex.org/W2030036522","doi":"https://doi.org/10.1007/bf01582244","title":"Properties of a representation of a basis for the null space","display_name":"Properties of a representation of a basis for the null space","publication_year":1985,"publication_date":"1985-11-01","ids":{"openalex":"https://openalex.org/W2030036522","doi":"https://doi.org/10.1007/bf01582244","mag":"2030036522"},"language":"en","primary_location":{"id":"doi:10.1007/bf01582244","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01582244","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003732991","display_name":"Philip E. Gill","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Philip E. Gill","raw_affiliation_strings":["Department of Operations Research, Stanford University, 94305, Stanford, CA, USA","Dept. of Operations Research, Stanford University, Stanford, USA"],"affiliations":[{"raw_affiliation_string":"Department of Operations Research, Stanford University, 94305, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Dept. of Operations Research, Stanford University, Stanford, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109312645","display_name":"Walter Murray","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Walter Murray","raw_affiliation_strings":["Department of Operations Research, Stanford University, 94305, Stanford, CA, USA","Dept. of Operations Research, Stanford University, Stanford, USA"],"affiliations":[{"raw_affiliation_string":"Department of Operations Research, Stanford University, 94305, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Dept. of Operations Research, Stanford University, Stanford, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039807799","display_name":"Michael A. Saunders","orcid":"https://orcid.org/0000-0003-3800-4982"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael A. Saunders","raw_affiliation_strings":["Department of Operations Research, Stanford University, 94305, Stanford, CA, USA","Dept. of Operations Research, Stanford University, Stanford, USA"],"affiliations":[{"raw_affiliation_string":"Department of Operations Research, Stanford University, 94305, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Dept. of Operations Research, Stanford University, Stanford, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110533470","display_name":"G. W. Stewart","orcid":null},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"G. W. Stewart","raw_affiliation_strings":["Department of Computer Science and Institute for Physical Science and Technology, University of Maryland, 20742, College Park, MD, USA","Department of Computer Science and Institute for Physical Science and Technology, University of Maryland, College Park, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Institute for Physical Science and Technology, University of Maryland, 20742, College Park, MD, USA","institution_ids":["https://openalex.org/I66946132"]},{"raw_affiliation_string":"Department of Computer Science and Institute for Physical Science and Technology, University of Maryland, College Park, USA","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103458692","display_name":"Margaret H. Wright","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Margaret H. Wright","raw_affiliation_strings":["Department of Operations Research, Stanford University, 94305, Stanford, CA, USA","Dept. of Operations Research, Stanford University, Stanford, USA"],"affiliations":[{"raw_affiliation_string":"Department of Operations Research, Stanford University, 94305, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Dept. of Operations Research, Stanford University, Stanford, USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5003732991"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.5683,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.82854545,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"33","issue":"2","first_page":"172","last_page":"186"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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":0.9993000030517578,"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"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.98580002784729,"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/mathematics","display_name":"Mathematics","score":0.8676242828369141},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.6037885546684265},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5687363147735596},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5528591871261597},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5333998203277588},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.528071403503418},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5181999802589417},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5115176439285278},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4940057396888733},{"id":"https://openalex.org/keywords/null","display_name":"Null (SQL)","score":0.4809757471084595},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4516904652118683},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4511442184448242},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3851158618927002},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3343648314476013},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2859081029891968},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15409770607948303},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08489957451820374}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8676242828369141},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.6037885546684265},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5687363147735596},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5528591871261597},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5333998203277588},{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.528071403503418},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5181999802589417},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5115176439285278},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4940057396888733},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.4809757471084595},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4516904652118683},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4511442184448242},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3851158618927002},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3343648314476013},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2859081029891968},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15409770607948303},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08489957451820374},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/bf01582244","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01582244","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:ADA157681","is_oa":false,"landing_page_url":"http://oai.dtic.mil/oai/oai?&verb=getRecord&metadataPrefix=html&identifier=ADA157681","pdf_url":null,"source":{"id":"https://openalex.org/S4406923043","display_name":"Defense Technical Information Center (DTIC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"DTIC AND NTIS","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W346901071","https://openalex.org/W1516152711","https://openalex.org/W1970377488","https://openalex.org/W2021200576","https://openalex.org/W2069624410","https://openalex.org/W2070513764","https://openalex.org/W2082314805","https://openalex.org/W2082709304","https://openalex.org/W2135622428","https://openalex.org/W4244131331"],"related_works":["https://openalex.org/W1485846902","https://openalex.org/W3037218165","https://openalex.org/W2075768550","https://openalex.org/W3022218857","https://openalex.org/W2369178846","https://openalex.org/W2982181895","https://openalex.org/W2082716031","https://openalex.org/W2951287487","https://openalex.org/W2990085810","https://openalex.org/W2084348954"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}