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Start Over Creator Jun, Young-Bae

1. Invertible commutativity preservers of matrices over max algebra

Creator:
Song, Seok-Zun, Kang, Kyung-Tae, and Jun, Young-Bae
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
max algebra, linear operator, and pair of commuting matrices
Language:
English
Description:
The max algebra consists of the nonnegative real numbers equipped with two binary operations, maximization and multiplication. We characterize the invertible linear operators that preserve the set of commuting pairs of matrices over a subalgebra of max algebra.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Perimeter preserver of matrices over semifields

Creator:
Song, Seok-Zun, Kang, Kyung-Tae, and Jun, Young-Bae
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
linear operator, rank, dominate, perimeter, and $(U,V)$-operator
Language:
English
Description:
For a rank-$1$ matrix $A= {\bold a \bold b}^t$, we define the perimeter of $A$ as the number of nonzero entries in both $\bold a$ and $\bold b$. We characterize the linear operators which preserve the rank and perimeter of rank-$1$ matrices over semifields. That is, a linear operator $T$ preserves the rank and perimeter of rank-$1$ matrices over semifields if and only if it has the form $T(A)=U A V$, or $T(A)=U A^t V$ with some invertible matrices U and V.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public