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Linear preserver of n × 1 Ferrers vectors
Let A = [ a ij ] m × n be an m × n matrix of zeros and ones. The matrix A is said to be a Ferrers matrix if it has decreasing row sums and it is row and...
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Explicit Solutions of Infinite Linear Systems Associated with Group Inverse Endomorphisms
The aim of this note is to offer an algorithm for studying solutions of infinite linear systems associated with group inverse endomorphisms. As...
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Row Hadamard majorization on Mm,n
An m × n matrix R with nonnegative entries is called row stochastic if the sum of entries on every row of R is 1. Let M m,n be the set of all m × n ...
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(0, 1)-Matrices, Discrepancy and Preservers
Let m and n be positive integers, and let R = ( r 1 , . . . , r m ) and S = ( s 1 , . . . , s n ) be nonnegative integral vectors. Let A ( R , S ) be the set of all m ...
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Centralizing additive maps on rank r block triangular matrices
Let F be a field and let k, n 1 , …, n k be positive integers with n 1 + … + n k = n ≥ 2. We denote by T n1 ,…, n k a block triangular matrix algebra over F...
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On Linear Preservers of Two-Sided Gut-Majorization On Mn,m
For X , Y ∈ M n , m it is said that X is gut-majorized by Y , and we write X ≺ gut Y , if there exists an n -by- n upper triangular g-row stochastic matrix R ...
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The a-Number of Hyperelliptic Curves
It is known that for a smooth hyperelliptic curve to have a large a-number, the genus must be small relative to the characteristic of the field,...
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Additive maps preserving the scrambling index are bijective
We prove that additive transformations on matrices over the binary Boolean semiring that preserve the scrambling index are automatically bijective....
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Linear preservers of row-dense matrices
Let M m , n be the set of all m × n real matrices. A matrix A ∈ M m , n is said to be row-dense if there are no zeros between two nonzero entries for...
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Unitary Similarity Preserving Linear Maps on B(H)
We determine all bijective unitary similarity preserving linear maps on B ( H ), the algebra of all bounded linear operators on a separable...
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Linear operators that preserve graphical properties of matrices: Isolation numbers
Let A be a Boolean {0, 1} matrix. The isolation number of A is the maximum number of ones in A such that no two are in any row or any column (that is...
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Ut-Majorization on \( {\mathbb{R}}^{n} \) and its Linear Preservers
Let \( {M_n} \) be the set of all...
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The group of commutativity preserving maps on strictly upper triangular matrices
Let N = N n ( R ) be the algebra of all n × n strictly upper triangular matrices over a unital commutative ring R . A map φ on N is called preserving...
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Linear operators that preserve Boolean rank of Boolean matrices
The Boolean rank of a nonzero m × n Boolean matrix A is the minimum number k such that there exist an m× k Boolean matrix B and a k × n Boolean...