{"created":"2023-06-20T15:45:38.408653+00:00","id":146,"links":{},"metadata":{"_buckets":{"deposit":"cf6e4e65-5f37-4c22-9e39-cb36f9f52785"},"_deposit":{"created_by":4,"id":"146","owners":[4],"pid":{"revision_id":0,"type":"depid","value":"146"},"status":"published"},"_oai":{"id":"oai:hama-med.repo.nii.ac.jp:00000146","sets":["6:14:23"]},"author_link":["490"],"control_number":"146","item_2_biblio_info_5":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"1987-03-31","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"1","bibliographicPageEnd":"22","bibliographicPageStart":"19","bibliographic_titles":[{"bibliographic_title":"浜松医科大学紀要. 一般教育","bibliographic_titleLang":"ja"},{"bibliographic_title":"Reports of Liberal Arts, Hamamatsu University School of Medicine","bibliographic_titleLang":"en"}]}]},"item_2_description_9":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"Let K be a commutative ring. For each n×n matrix A=(aij) over K, we define the determinant d(A) by the formula\n          d(A)=Σσ ε(σ)a(σ),\nwhere the sum is taken over the set Sn of all permutations σ of {1,2,…,n}, ε(σ) is the sign of the permutation, and\n          a(σ)=a1σ(1)a2σ(2)…anσ(n)\nAssume n≧2, and let τ be a transposition in Sn. The mapping γτ: Sn→Sn by the formula γτ(σ)=στ for each σ∈Sn is a bijection. Then it is clear that the following theorem holds : \n   Theorem. d(A) = Σσ (a(σ)-a(στ)), \nwhere the sum is taken over the set An of all even permutations σ.\nIn this paper, we will show that next two essential theorems B2 and C1 can be derived from our theorem.\n   Theorem B2. Interchanging two rows of A multiplies d(A) by -1.\n   Theorem C1. If A has two rows alike, then d(A)=0.","subitem_description_language":"en","subitem_description_type":"Abstract"}]},"item_2_publisher_6":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"浜松医科大学","subitem_publisher_language":"ja"}]},"item_2_source_id_19":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"0914-0174","subitem_source_identifier_type":"PISSN"}]},"item_2_source_id_23":{"attribute_name":"NII書誌ID","attribute_value_mlt":[{"subitem_source_identifier":"AN10032827","subitem_source_identifier_type":"NCID"}]},"item_2_version_type_32":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_970fb48d4fbd8a85","subitem_version_type":"VoR"}]},"item_access_right":{"attribute_name":"アクセス権","attribute_value_mlt":[{"subitem_access_right":"open access","subitem_access_right_uri":"http://purl.org/coar/access_right/c_abf2"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"伊藤, 善彦","creatorNameLang":"ja"}],"nameIdentifiers":[{"nameIdentifier":"490","nameIdentifierScheme":"WEKO"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2018-08-27"}],"displaytype":"detail","filename":"kiyo01_02.pdf","filesize":[{"value":"107.6 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"kiyo01_02.pdf","url":"https://hama-med.repo.nii.ac.jp/record/146/files/kiyo01_02.pdf"},"version_id":"184b457a-af6d-4290-84a9-8d050fc42504"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"行列式の基本性質","subitem_subject_language":"ja","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"行列式の基本性質について","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"行列式の基本性質について","subitem_title_language":"ja"},{"subitem_title":"A Remark on the Essential Properties of Determinants","subitem_title_language":"en"}]},"item_type_id":"2","owner":"4","path":["23"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2013-08-27"},"publish_date":"2013-08-27","publish_status":"0","recid":"146","relation_version_is_last":true,"title":["行列式の基本性質について"],"weko_creator_id":"4","weko_shared_id":-1},"updated":"2024-02-05T07:25:45.692170+00:00"}