Volume 6, Issue 2 (11-2011)                   IJMSI 2011, 6(2): 43-50 | Back to browse issues page

DOI: 10.7508/ijmsi.2011.02.005

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Khalooei F, Salemi A. Linear Preservers of Majorization. IJMSI. 2011; 6 (2) :43-50
URL: http://ijmsi.ir/article-1-236-en.html


For vectors $X, Yin mathbb{R}^{n}$, we say $X$ is left matrix majorized by $Y$ and write $X prec_{ell} Y$ if for some row stochastic matrix $R, ~X=RY.$ Also, we write $Xsim_{ell}Y,$ when $Xprec_{ell}Yprec_{ell}X.$ A linear operator $Tcolon mathbb{R}^{p}to mathbb{R}^{n}$ is said to be a linear preserver of a given relation $prec$ if $Xprec Y$ on $mathbb{R}^{p}$ implies that $TXprec TY$ on $mathbb{R}^{n}$. In this note we study linear preservers of $sim_{ell}$ from $mathbb{R}^{p}$ to $mathbb{R}^{n}.$ In particular, we characterize all linear preservers of $sim_{ell}$ from $mathbb{R}^{2}$ to $mathbb{R}^{n},$ and also, all linear preservers of $sim_{ell}$ from $mathbb{R}^{p}$ to $mathbb{R}^{p}.$

Type of Study: Research | Subject: General

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