{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T15:07:51Z","timestamp":1648566471525},"reference-count":4,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2008,3]]},"abstract":"<jats:p> In this paper, we study the irreducible decompositions of the degeneracy loci of matrices which are defined by rank conditions on upper left submatrices. By introducing the concepts of standard and essential rank functions, we give an explicit classification of these degeneracy loci. Based on standard rank functions, we design an algorithm to write a degeneracy locus as a union of its irreducible components. This gives an answer to a problem raised by Sturmfels. <\/jats:p>","DOI":"10.1142\/s0218196708004433","type":"journal-article","created":{"date-parts":[[2008,3,20]],"date-time":"2008-03-20T09:29:16Z","timestamp":1206005356000},"page":"257-270","source":"Crossref","is-referenced-by-count":0,"title":["IRREDUCIBLE DECOMPOSITIONS OF DEGENERACY LOCI OF MATRICES"],"prefix":"10.1142","volume":"18","author":[{"given":"XU-AN","family":"ZHAO","sequence":"first","affiliation":[{"name":"Department of Mathematics, Beijing Normal University, Beijing 100875, China"}]},{"given":"HONGZHU","family":"GAO","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Beijing Normal University, Beijing 100875, China"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-96-08502-6"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-92-06516-1"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0096380"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3849-0"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196708004433","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T22:28:43Z","timestamp":1565130523000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196708004433"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,3]]},"references-count":4,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2008,3]]}},"alternative-id":["10.1142\/S0218196708004433"],"URL":"https:\/\/doi.org\/10.1142\/s0218196708004433","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,3]]}}}