Volume 11, Issue 2 (11-2016)                   IJMSI 2016, 11(2): 111-118 | Back to browse issues page

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Ilkhanizadeh Manesh A. Linear Functions Preserving Sut-Majorization on RN. IJMSI. 2016; 11 (2) :111-118
URL: http://ijmsi.ir/article-1-549-en.html

Suppose $textbf{M}_{n}$ is the vector space of all $n$-by-$n$ real matrices, and let $mathbb{R}^{n}$ be the set of all $n$-by-$1$ real vectors. A matrix $Rin textbf{M}_{n}$ is said to be $textit{row substochastic}$ if it has nonnegative entries and each row sum is at most $1$. For $x$, $y in mathbb{R}^{n}$, it is said that $x$ is $textit{sut-majorized}$ by $y$ (denoted by $ xprec_{sut} y$) if there exists an $n$-by-$n$ upper triangular row substochastic matrix $R$ such that $x=Ry$. In this note, we characterize the linear functions $T$ : $mathbb{R}^n$ $rightarrow$ $mathbb{R}^n$ preserving (resp. strongly preserving) $prec_{sut}$ with additional condition $Te_{1}neq 0$ (resp. no additional conditions).

Type of Study: Research paper | Subject: Special

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