Induced Maps on Matrices over Fields
Suppose that 𝔽 is a field and m,n≥3 are integers. Denote by Mmn(𝔽) the set of all m×n matrices over 𝔽 and by Mn(𝔽) the set Mnn(𝔽). Let fij (i∈[1,m],j∈[1,n]) be functions on 𝔽, where [1,n] stands for the set {1,…,n}. We say that a map f:Mmn(𝔽)→Mmn(𝔽) is induced by {fij} if f is defined by f:[aij]↦[fi...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/596756 |
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| author | Li Yang Xuezhi Ben Ming Zhang Chongguang Cao |
| author_facet | Li Yang Xuezhi Ben Ming Zhang Chongguang Cao |
| author_sort | Li Yang |
| collection | DOAJ |
| description | Suppose that 𝔽 is a field and m,n≥3 are integers. Denote by Mmn(𝔽) the set of all m×n matrices over 𝔽 and by Mn(𝔽) the set Mnn(𝔽). Let fij (i∈[1,m],j∈[1,n]) be functions on 𝔽, where [1,n] stands for the set {1,…,n}. We say that a map f:Mmn(𝔽)→Mmn(𝔽) is induced by {fij} if f is defined by f:[aij]↦[fij(aij)]. We say that a map f on Mn(𝔽) preserves similarity if A~B⇒f(A)~f(B), where A~B represents that A and B are similar. A map f on Mn(𝔽) preserving inverses of matrices means f(A)f(A-1)=In for every invertible A∈Mn(𝔽). In this paper, we characterize induced maps preserving similarity and inverses of matrices, respectively. |
| format | Article |
| id | doaj-art-9a462aa1b3bb4a4586b114c6aa8e849c |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-9a462aa1b3bb4a4586b114c6aa8e849c2025-02-03T05:46:45ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/596756596756Induced Maps on Matrices over FieldsLi Yang0Xuezhi Ben1Ming Zhang2Chongguang Cao3Department of Foundation, Harbin Finance University, Harbin 150030, ChinaSchool of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaSchool of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaSchool of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaSuppose that 𝔽 is a field and m,n≥3 are integers. Denote by Mmn(𝔽) the set of all m×n matrices over 𝔽 and by Mn(𝔽) the set Mnn(𝔽). Let fij (i∈[1,m],j∈[1,n]) be functions on 𝔽, where [1,n] stands for the set {1,…,n}. We say that a map f:Mmn(𝔽)→Mmn(𝔽) is induced by {fij} if f is defined by f:[aij]↦[fij(aij)]. We say that a map f on Mn(𝔽) preserves similarity if A~B⇒f(A)~f(B), where A~B represents that A and B are similar. A map f on Mn(𝔽) preserving inverses of matrices means f(A)f(A-1)=In for every invertible A∈Mn(𝔽). In this paper, we characterize induced maps preserving similarity and inverses of matrices, respectively.http://dx.doi.org/10.1155/2014/596756 |
| spellingShingle | Li Yang Xuezhi Ben Ming Zhang Chongguang Cao Induced Maps on Matrices over Fields Abstract and Applied Analysis |
| title | Induced Maps on Matrices over Fields |
| title_full | Induced Maps on Matrices over Fields |
| title_fullStr | Induced Maps on Matrices over Fields |
| title_full_unstemmed | Induced Maps on Matrices over Fields |
| title_short | Induced Maps on Matrices over Fields |
| title_sort | induced maps on matrices over fields |
| url | http://dx.doi.org/10.1155/2014/596756 |
| work_keys_str_mv | AT liyang inducedmapsonmatricesoverfields AT xuezhiben inducedmapsonmatricesoverfields AT mingzhang inducedmapsonmatricesoverfields AT chongguangcao inducedmapsonmatricesoverfields |