Hyperbolicity preservers and majorization

Linear Preservers of Majorization

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 $mathb...

Latin-majorization and its linear preservers

In this paper we study the concept of Latin-majorizati-\on. Geometrically this concept is different from other kinds of majorization in some aspects. Since the set of all $x$s Latin-majorized by a fixed $y$ is not convex, but, consists of union of finitely many convex sets. Next, we hint to linear preservers of Latin-majorization on $ mathbb{R}^{n}$ and ${M_{n,m}}$.

Linear preservers of two-sided matrix majorization

For vectors X, <span style="fon...

On Nonlinear Preservers of Weak Matrix Majorization

SGLT-MAJORIZATION ON Mn,m AND ITS LINEAR PRESERVERS

A matrix R is said to be g-row substochastic if Re ≤ e. For X, Y ∈ Mn,m, it is said that X is sglt-majorized by Y , X ≺sglt Y , if there exists an n-by-n lower triangular g-row substochastic matrix R such that X = RY . This paper characterizes all (strong) linear preservers and strong linear preservers of ≺sglt on Rn and Mn,m, respectively.