Linear mappings preserving square-zero matrices
نویسندگان
چکیده
منابع مشابه
Linear maps preserving or strongly preserving majorization on matrices
For $A,Bin M_{nm},$ we say that $A$ is left matrix majorized (resp. left matrix submajorized) by $B$ and write $Aprec_{ell}B$ (resp. $Aprec_{ell s}B$), if $A=RB$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $R.$ Moreover, we define the relation $sim_{ell s} $ on $M_{nm}$ as follows: $Asim_{ell s} B$ if $Aprec_{ell s} Bprec_{ell s} A.$ This paper characterizes all linear p...
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Let A be a matrix over the integers, and let p be a positive integer. A submatrix B of A is zero-sum mod p if the sum of each row of B and the sum of each column of B is a multiple of p. Let M(p, k) denote the least integer m for which every square matrix of order at least m has a square submatrix of order k which is zero-sum mod p. In this paper we supply upper and lower bounds for M(p, k). In...
متن کاملlinear maps preserving or strongly preserving majorization on matrices
for $a,bin m_{nm},$ we say that $a$ is left matrix majorized (resp. left matrix submajorized) by $b$ and write $aprec_{ell}b$ (resp. $aprec_{ell s}b$), if $a=rb$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $r.$ moreover, we define the relation $sim_{ell s} $ on $m_{nm}$ as follows: $asim_{ell s} b$ if $aprec_{ell s} bprec_{ell s} a.$ this paper characterizes all linear p...
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Let Mn be the set of n × n complex matrices, and for every A ∈ Mn, let Sp(A) denote the spectrum of A. For various types of products A1 ∗ · · · ∗ Ak on Mn, it is shown that a mapping φ : Mn → Mn satisfying Sp(A1 ∗ · · · ∗ Ak) = Sp(φ(A1) ∗ · · · ∗ φ(Ak)) for all A1, . . . , Ak ∈ Mn has the form X → ξS−1XS or A → ξS−1XtS for some invertible S ∈ Mn and scalar ξ. The result covers the special cases...
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Let D be a division ring and let m,n be integers ≥ 2. Let Mm×n(D) be the space of m × n matrices. In the fundamental theorem of the geometry of rectangular matrices all bijective mappings φ of Mm×n(D) are determined such that both φ and φ−1 preserve adjacency. We show that if a bijective map φ of Mm×n(D) preserves the adjacency then also φ −1 preserves the adjacency. Thus the supposition that φ...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1993
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700015811