{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T08:47:41Z","timestamp":1765961261280,"version":"3.48.0"},"reference-count":28,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Skew-symmetric matrices of order 7 defined through the 2-fold vector cross product in \u2102\n                    <jats:sup>7<\/jats:sup>\n                    , and other related matrices, are presented. More concretely, matrix properties, namely invertibility, nullspace, powers and index, are studied. As a consequence, results on vector cross product equations, vector cross product differential equations and vector cross product difference equations in \u2102\n                    <jats:sup>7<\/jats:sup>\n                    are established.\n                  <\/jats:p>","DOI":"10.2478\/auom-2023-0003","type":"journal-article","created":{"date-parts":[[2025,2,6]],"date-time":"2025-02-06T05:52:42Z","timestamp":1738821162000},"page":"47-69","source":"Crossref","is-referenced-by-count":0,"title":["Skew-symmetric matrices related to the vector cross product in \u2102\n                    <sup>7<\/sup>"],"prefix":"10.2478","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0266-7055","authenticated-orcid":false,"given":"P. D.","family":"Beites","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica and CMA-UBI Universidade da Beira Interior R . Marqu\u00eas d\u2019\u00c1vila e Bolama 6201-001 Covilh\u00e3 , Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6499-0072","authenticated-orcid":false,"given":"A. P.","family":"Nicol\u00e1s","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas , Universidad de Oviedo Calle Federico Garc\u00eda Lorca , Oviedo , Espa\u00f1a"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3964-2425","authenticated-orcid":false,"given":"Jos\u00e9","family":"Vit\u00f3ria","sequence":"additional","affiliation":[{"name":"University of Coimbra , Department of Mathematics Largo D. Dinis 3000-143 Coimbra , Portugal"}]}],"member":"374","published-online":{"date-parts":[[2023,2,4]]},"reference":[{"key":"2025121708382133272_j_auom-2023-0003_ref_001","unstructured":"[1] P. D. Beites, P. Catarino, On the Leonardo quaternion sequence. (2021), submitted."},{"key":"2025121708382133272_j_auom-2023-0003_ref_002","doi-asserted-by":"crossref","unstructured":"[2] P. D. Beites, A. P. Nicol\u00e1s, A note on standard composition algebras of types II and III. Advances in Applied Clifford Algebras 27 (2017), 955\u2013964.","DOI":"10.1007\/s00006-016-0668-8"},{"key":"2025121708382133272_j_auom-2023-0003_ref_003","doi-asserted-by":"crossref","unstructured":"[3] P. D. Beites, A. P. Nicol\u00e1s, P. Saraiva, J. Vit\u00f3ria, Vector cross product differential and difference equations in \u211d3 and in \u211d7. Electronic Journal of Linear Algebra 34 (2018), 675\u2013686.","DOI":"10.13001\/1081-3810.3843"},{"key":"2025121708382133272_j_auom-2023-0003_ref_004","doi-asserted-by":"crossref","unstructured":"[4] P. D. Beites, A. P. Nicol\u00e1s, J. Vit\u00f3ria, On skew-symmetric matrices related to the vector cross product in \u211d7. Electronic Journal of Linear Algebra 32 (2017), 138\u2013150.","DOI":"10.13001\/1081-3810.3498"},{"key":"2025121708382133272_j_auom-2023-0003_ref_005","doi-asserted-by":"crossref","unstructured":"[5] P. D. Beites, A. P. Nicol\u00e1s, J. 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