Displaying similar documents to “Computing the greatest 𝐗 -eigenvector of a matrix in max-min algebra”

On linear preservers of two-sided gut-majorization on 𝐌 n , m

Asma Ilkhanizadeh Manesh, Ahmad Mohammadhasani (2018)

Czechoslovak Mathematical Journal

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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 such that X = R Y . Define the relation gut as follows. X gut Y if X is gut-majorized by Y and Y is gut-majorized by X . The (strong) linear preservers of gut on n and strong linear preservers of this relation on 𝐌 n , m have been characterized before. This paper characterizes all (strong) linear preservers and strong linear preservers of gut on n and 𝐌 n , m .

Distance matrices perturbed by Laplacians

Balaji Ramamurthy, Ravindra Bhalchandra Bapat, Shivani Goel (2020)

Applications of Mathematics

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Let T be a tree with n vertices. To each edge of T we assign a weight which is a positive definite matrix of some fixed order, say, s . Let D i j denote the sum of all the weights lying in the path connecting the vertices i and j of T . We now say that D i j is the distance between i and j . Define D : = [ D i j ] , where D i i is the s × s null matrix and for i j , D i j is the distance between i and j . Let G be an arbitrary connected weighted graph with n vertices, where each weight is a positive definite matrix of order...

Theoretical analysis for 1 - 2 minimization with partial support information

Haifeng Li, Leiyan Guo (2025)

Applications of Mathematics

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We investigate the recovery of k -sparse signals using the 1 - 2 minimization model with prior support set information. The prior support set information, which is believed to contain the indices of nonzero signal elements, significantly enhances the performance of compressive recovery by improving accuracy, efficiency, reducing complexity, expanding applicability, and enhancing robustness. We assume k -sparse signals 𝐱 with the prior support T which is composed of g true indices and b wrong...

On row-sum majorization

Farzaneh Akbarzadeh, Ali Armandnejad (2019)

Czechoslovak Mathematical Journal

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Let 𝕄 n , m be the set of all n × m real or complex matrices. For A , B 𝕄 n , m , we say that A is row-sum majorized by B (written as A rs B ) if R ( A ) R ( B ) , where R ( A ) is the row sum vector of A and is the classical majorization on n . In the present paper, the structure of all linear operators T : 𝕄 n , m 𝕄 n , m preserving or strongly preserving row-sum majorization is characterized. Also we consider the concepts of even and circulant majorization on n and then find the linear preservers of row-sum majorization of these relations on 𝕄 n , m . ...

( 0 , 1 ) -matrices, discrepancy and preservers

LeRoy B. Beasley (2019)

Czechoslovak Mathematical Journal

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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 × n ( 0 , 1 ) -matrices with row sum vector R and column vector S . Let R and S be nonincreasing, and let F ( R ) be the m × n ( 0 , 1 ) -matrix, where for each i , the i th row of F ( R , S ) consists of r i 1’s followed by ( n - r i ) 0’s. Let A A ( R , S ) . The discrepancy of A, disc ( A ) , is the number of positions in which F ( R ) has a 1 and A has a 0. In this paper we investigate linear operators mapping m × n matrices over...

Sum-product theorems and incidence geometry

Mei-Chu Chang, Jozsef Solymosi (2007)

Journal of the European Mathematical Society

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In this paper we prove the following theorems in incidence geometry. 1. There is δ > 0 such that for any P 1 , , P 4 , and Q 1 , , Q n 2 , if there are n ( 1 + δ ) / 2 many distinct lines between P i and Q j for all i , j , then P 1 , , P 4 are collinear. If the number of the distinct lines is < c n 1 / 2 then the cross ratio of the four points is algebraic. 2. Given c > 0 , there is δ > 0 such that for any P 1 , P 2 , P 3 2 noncollinear, and Q 1 , , Q n 2 , if there are c n 1 / 2 many distinct lines between P i and Q j for all i , j , then for any P 2 { P 1 , P 2 , P 3 } , we have δ n distinct lines between P and Q j . 3. Given...

𝒞 k -regularity for the ¯ -equation with a support condition

Shaban Khidr, Osama Abdelkader (2017)

Czechoslovak Mathematical Journal

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Let D be a 𝒞 d q -convex intersection, d 2 , 0 q n - 1 , in a complex manifold X of complex dimension n , n 2 , and let E be a holomorphic vector bundle of rank N over X . In this paper, 𝒞 k -estimates, k = 2 , 3 , , , for solutions to the ¯ -equation with small loss of smoothness are obtained for E -valued ( 0 , s ) -forms on D when n - q s n . In addition, we solve the ¯ -equation with a support condition in 𝒞 k -spaces. More precisely, we prove that for a ¯ -closed form f in 𝒞 0 , q k ( X D , E ) , 1 q n - 2 , n 3 , with compact support and for ε with 0 < ε < 1 there...

Complex series and connected sets

B. Jasek

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CONTENTSPREFACE..........................................................................................................................................................................3INTRODUCTION............................................................................................................................................................. 41. Notation. 2. Subject of the paper.Chapter I. DECOMPOSITION OF Σ INTO Σ 1 , Σ 2 , Σ 3 , Σ 4 INESSENTIAL RESTRICTIONOF GENERALITY ...............................................................................................................................................................