LINEAR PRESERVERS OF BOOLEAN RANK BETWEEN DIFFERENT MATRIX SPACES
نویسندگان
چکیده
منابع مشابه
linear preservers of two-sided matrix majorization
for vectors x, y ∈ rn, it is said that x is left matrix majorizedby y if for some row stochastic matrix r; x = ry. the relationx ∼` y, is defined as follows: x ∼` y if and only if x is leftmatrix majorized by y and y is left matrix majorized by x. alinear operator t : rp → rn is said to be a linear preserver ofa given relation ≺ if x ≺ y on rp implies that t x ≺ ty onrn. the linear preservers o...
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Let F be a field and m,n be integers m,n > 3. Let SMn(F) and STn(F) denote the linear space of n × n per-symmetric matrices over F and the linear space of n × n per-symmetric triangular matrices over F, respectively. In this note, the structure of spaces of bounded rank-two matrices of STn(F) is determined. Using this structural result, a classification of bounded rank-two linear preservers ψ :...
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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...
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The famous shortest path tree lemma states that, for any node s in a graph G = (V,E), there is a subgraph on O(n) edges that preserves all distances between node pairs in the set {s}×V . A very basic question in distance sketching research, with applications to other problems in the field, is to categorize when else graphs admit sparse subgraphs that preserve distances between a set P of p node...
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ژورنال
عنوان ژورنال: Journal of the Korean Mathematical Society
سال: 2015
ISSN: 0304-9914
DOI: 10.4134/jkms.2015.52.3.625