논문KCI 등재
INJECTIVE LINEAR MAPS ON T1(F) THAT PRESERVE THE ADDITIVITY OF RANK
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초록
We consider $\mc T_\infty(F)$ -- the space of upper triangular infinite matrices over a field $F$. We investigate injective linear maps on this space which preserve the additivity of rank, i.e., the maps $\phi$ such that \linebreak $\rank(x+y)=\rank(x)+\rank(y)$ implies $\rank(\phi(x+y))=\rank(\phi(x))+\rank(\phi(y))$ for all $x$, $y\in\mc T_\infty(F)$.
Abstract
We consider $\mc T_\infty(F)$ -- the space of upper triangular infinite matrices over a field $F$. We investigate injective linear maps on this space which preserve the additivity of rank, i.e., the maps $\phi$ such that \linebreak $\rank(x+y)=\rank(x)+\rank(y)$ implies $\rank(\phi(x+y))=\rank(\phi(x))+\rank(\phi(y))$ for all $x$, $y\in\mc T_\infty(F)$.
참고문헌 (16)
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관련 논문AI추천
Linear rank preservers on infinite triangular matricesRoksana Slowik대한수학회 · 대한수학회지2016 · 제53권 제1호Linear transformations that preserve term rank between different matrix spaces송석준, LeRoy B. Beasley대한수학회 · 대한수학회지2013 · 제50권 제1호Linear preservers of spanning column rank of matrix sums over semirings송석준대한수학회 · 대한수학회지2008 · 제45권 제2호LINEAR PRESERVERS OF BOOLEAN RANK BETWEEN DIFFERENT MATRIX SPACES강경태, 송석준, Leroy B. Beasley대한수학회 · 대한수학회지2015 · 제52권 제3호COMPOUND-COMMUTING ADDITIVE MAPS ON MATRIX SPACESWai Leong Chooi대한수학회 · 대한수학회지2011 · 제48권 제1호Linear preservers of spanning column rank of matrix products over semirings송석준, 전영배, 천기상대한수학회 · 대한수학회지2008 · 제45권 제4호
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