{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T09:38:00Z","timestamp":1775468280897,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We prove, by simple manipulation of commutators, two noncommutative generalizations of the Cauchy\u2013Binet formula for the determinant of a product.  As special cases we obtain elementary proofs of the Capelli identity from classical invariant theory and of Turnbull's Capelli-type identities for symmetric and antisymmetric matrices.<\/jats:p>","DOI":"10.37236\/192","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:27:27Z","timestamp":1578716847000},"source":"Crossref","is-referenced-by-count":10,"title":["Noncommutative determinants, Cauchy&amp;ndash;Binet formulae, and Capelli-type identities I. Generalizations of the Capelli and Turnbull identities"],"prefix":"10.37236","volume":"16","author":[{"given":"Sergio","family":"Caracciolo","sequence":"first","affiliation":[]},{"given":"Alan D.","family":"Sokal","sequence":"additional","affiliation":[]},{"given":"Andrea","family":"Sportiello","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,8,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r103\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r103\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T02:41:43Z","timestamp":1579315303000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r103"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,8,7]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/192","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,8,7]]},"article-number":"R103"}}