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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 한국전산응용수학회 Journal of applied mathematics & informatics Journal of applied mathematics & informatics 제27권 제1호
- 발행연도
- 2009.1
- 수록면
- 97 - 103 (7page)
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초록· 키워드
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Suppose F is a field of characteristic not 2 and $F\;{\neq}\;Z_3$. Let $M_n(F)$ be the linear space of all $n{\times}n$ matrices over F, and let ${\Gamma}_n(F)$ be the subset of $M_n(F)$ consisting of all $n{\times}n$ involutory matrices. We denote by ${\Phi}_n(F)$ the set of all maps from $M_n(F)$ to itself satisfying A - ${\lambda}B{\in}{\Gamma}_n(F)$ if and only if ${\phi}(A)$ - ${\lambda}{\phi}(B){\in}{\Gamma}_n(F)$ for every A, $B{\in}M_n(F)$ and ${\lambda}{\in}F$. It was showed that ${\phi}{\in}{\Phi}_n(F)$ if and only if there exist an invertible matrix $P{\in}M_n(F)$ and an involutory element ${\varepsilon}$ such that either ${\phi}(A)={\varepsilon}PAP^{-1}$ for every $A{\in}M_n(F)$ or ${\phi}(A)={\varepsilon}PA^{T}P^{-1}$ for every $A{\in}M_n(F)$. As an application, the maps preserving inverses of matrces also are characterized.
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참고문헌 (11)
참고문헌 신청
P. ˇ Semrl / 2003 / Hua’s fundamental theorems of the geometry of matrices and related results / Linear Algebra Appl 361:161~179
G. Dolinar / 2003 / Maps on matrix algebras preserving idempotents / Linear Algebra Appl 371:287~300
X. Zhang / 2004 / Idempotence-preserving maps without the linearity and surjectivity assumptions / Linear Algebra Appl 387:167~182
G. Dolinar / 2002 / Determinant preserving maps on matrix algebras / Linear Algebra Appl 348:189~192
G. Dolinar / 2004 / Maps on matrix algebras preserving commutativity / Linear and Multilinear Algebra 52:69~78
G. Dolinar / 2003 / Maps on matrix algebras preserving idempotents / Linear Algebra Appl 371:287~300
X. Zhang / 2004 / Idempotence-preserving maps without the linearity and surjectivity assumptions / Linear Algebra Appl 387:167~182
G. Dolinar / 2002 / Determinant preserving maps on matrix algebras / Linear Algebra Appl 348:189~192
G. Dolinar / 2004 / Maps on matrix algebras preserving commutativity / Linear and Multilinear Algebra 52:69~78
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