{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,1]],"date-time":"2025-06-01T04:15:52Z","timestamp":1748751352510},"reference-count":0,"publisher":"Wiley","issue":"63","license":[{"start":{"date-parts":[[2000,1,1]],"date-time":"2000-01-01T00:00:00Z","timestamp":946684800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["10271021"],"award-info":[{"award-number":["10271021"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2004,1]]},"abstract":"<jats:p>Denote by <jats:italic>&amp;#x1D4A6;<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>(<jats:bold>F<\/jats:bold>) the linear space of all \n<jats:italic>n<\/jats:italic> \u00d7 <jats:italic>n<\/jats:italic>\n alternate matrices over a field <jats:bold>F<\/jats:bold>. We first characterize all linear bijective maps on <jats:italic>&amp;#x1D4A6;<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>(<jats:bold>F<\/jats:bold>)(<jats:italic>n<\/jats:italic> \u2265 4) preserving rank 2 when <jats:bold>F<\/jats:bold> is any field, and thereby the characterization of all linear bijective maps on <jats:italic>&amp;#x1D4A6;<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>(<jats:bold>F<\/jats:bold>) preserving the max\u2010rank is done when <jats:bold>F<\/jats:bold> is any field\nexcept for {0, 1}\n. Furthermore, the linear preservers of the determinant (resp., adjoint) on \n<jats:italic>&amp;#x1D4A6;<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>(<jats:bold>F<\/jats:bold>) are also characterized by\nreducing them to the linear preservers of the max\u2010rank when <jats:italic>n<\/jats:italic>\n is even and <jats:bold>F<\/jats:bold>\n is any field except for {0, 1}. This paper can be viewed as a supplement version of several related results.<\/jats:p>","DOI":"10.1155\/s0161171204401161","type":"journal-article","created":{"date-parts":[[2004,11,30]],"date-time":"2004-11-30T16:22:51Z","timestamp":1101831771000},"page":"3409-3417","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Linear maps preserving rank 2 on the space of alternatematrices and their applications"],"prefix":"10.1155","volume":"2004","author":[{"given":"Chongguang","family":"Cao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaomin","family":"Tang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2004,11,30]]},"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2004\/808190.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/S0161171204401161","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T19:51:01Z","timestamp":1723060261000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/S0161171204401161"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1]]},"references-count":0,"journal-issue":{"issue":"63","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["10.1155\/S0161171204401161"],"URL":"https:\/\/doi.org\/10.1155\/s0161171204401161","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2004,1]]},"assertion":[{"value":"2004-01-18","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2004-11-30","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}