{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:16:46Z","timestamp":1760242606792,"version":"build-2065373602"},"reference-count":9,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2017,12,13]],"date-time":"2017-12-13T00:00:00Z","timestamp":1513123200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>We describe subspaces of generalized Hessenberg matrices where the determinant is convertible into the permanent by affixing \u00b1 signs. An explicit characterization of convertible Hessenberg-type matrices is presented. We conclude that convertible matrices with the maximum number of nonzero entries can be reduced to a basic set.<\/jats:p>","DOI":"10.3390\/math5040079","type":"journal-article","created":{"date-parts":[[2017,12,14]],"date-time":"2017-12-14T04:30:55Z","timestamp":1513225855000},"page":"79","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Convertible Subspaces of Hessenberg-Type Matrices"],"prefix":"10.3390","volume":"5","author":[{"given":"Henrique","family":"Da Cruz","sequence":"first","affiliation":[{"name":"Faculdade de Ci\u00eancias, Universidade da Beira Interior, Rua Marqu\u00eas d\u2019\u00c1vila e Bolama, 6201-001 Covilh\u00e3, Portugal"},{"name":"Centro de Matem\u00e1tica e Aplica\u00e7\u00f5es (CMA-UBI), Universidade da Beira Interior, Rua Marqu\u00eas d\u2019\u00c1vila e Bolama, 6201-001 Covilh\u00e3, Portugal"}]},{"given":"Ilda","family":"Rodrigues","sequence":"additional","affiliation":[{"name":"Faculdade de Ci\u00eancias, Universidade da Beira Interior, Rua Marqu\u00eas d\u2019\u00c1vila e Bolama, 6201-001 Covilh\u00e3, Portugal"}]},{"given":"Rog\u00e9rio","family":"Ser\u00f4dio","sequence":"additional","affiliation":[{"name":"Faculdade de Ci\u00eancias, Universidade da Beira Interior, Rua Marqu\u00eas d\u2019\u00c1vila e Bolama, 6201-001 Covilh\u00e3, Portugal"},{"name":"Centro de Matem\u00e1tica e Aplica\u00e7\u00f5es (CMA-UBI), Universidade da Beira Interior, Rua Marqu\u00eas d\u2019\u00c1vila e Bolama, 6201-001 Covilh\u00e3, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4772-4300","authenticated-orcid":false,"given":"Alberto","family":"Sim\u00f5es","sequence":"additional","affiliation":[{"name":"Faculdade de Ci\u00eancias, Universidade da Beira Interior, Rua Marqu\u00eas d\u2019\u00c1vila e Bolama, 6201-001 Covilh\u00e3, Portugal"},{"name":"Centro de Matem\u00e1tica e Aplica\u00e7\u00f5es (CMA-UBI), Universidade da Beira Interior, Rua Marqu\u00eas d\u2019\u00c1vila e Bolama, 6201-001 Covilh\u00e3, Portugal"},{"name":"Center for Research and Development in Mathematics and Applications (CIDMA), Universidade de Aveiro, Campus Universit\u00e1rio de Santiago, 3810-193 Aveiro, Portugal"}]},{"given":"Jos\u00e9","family":"Velhinho","sequence":"additional","affiliation":[{"name":"Faculdade de Ci\u00eancias, Universidade da Beira Interior, Rua Marqu\u00eas d\u2019\u00c1vila e Bolama, 6201-001 Covilh\u00e3, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2017,12,13]]},"reference":[{"key":"ref_1","first-page":"271","article-title":"Aufgabe 424","volume":"20","year":"1913","journal-title":"Arch. 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