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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 $x$, $y\in\mc T_\infty(F)$.
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참고문헌 (16)
참고문헌 신청
A. Guterman / 2001 / Linear preservers for matrix inequalities and partial orderings / Linear Algebra Appl 331 (1-3) : 75 ~ 87
G. Marsaglia / 1975 / Equalities and inequalities for ranks of matrices / Linear Multilinear Algebra 2 : 269 ~ 292
J. K. Baksalary / 1996 / A note on rank-additivity and range-additivity / Linear Algebra Appl 237-238 : 489 ~ 498
L. B. Beasley / 1981 / Linear operators which preserve pairs on which the rank is additive / J. Korean Soc. Ind. Appl. Maths 2 : 27 ~ 30
L. B. Beasley / 1996 / Spaces of matrices of equal rank / Linear Algebra Appl 40 : 183 ~ 187
G. Marsaglia / 1975 / Equalities and inequalities for ranks of matrices / Linear Multilinear Algebra 2 : 269 ~ 292
J. K. Baksalary / 1996 / A note on rank-additivity and range-additivity / Linear Algebra Appl 237-238 : 489 ~ 498
L. B. Beasley / 1981 / Linear operators which preserve pairs on which the rank is additive / J. Korean Soc. Ind. Appl. Maths 2 : 27 ~ 30
L. B. Beasley / 1996 / Spaces of matrices of equal rank / Linear Algebra Appl 40 : 183 ~ 187
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