Displaying similar documents to “A computation of positive one-peak posets that are Tits-sincere”

Linear preservers of rc-majorization on matrices

Mohammad Soleymani (2024)

Czechoslovak Mathematical Journal

Similarity:

Let A , B be n × m matrices. The concept of matrix majorization means the j th column of A is majorized by the j th column of B and this is done for all j by a doubly stochastic matrix D . We define rc-majorization that extended matrix majorization to columns and rows of matrices. Also, the linear preservers of rc-majorization will be characterized.

Controllable and tolerable generalized eigenvectors of interval max-plus matrices

Matej Gazda, Ján Plavka (2021)

Kybernetika

Similarity:

By max-plus algebra we mean the set of reals equipped with the operations a b = max { a , b } and a b = a + b for a , b . A vector x is said to be a generalized eigenvector of max-plus matrices A , B ( m , n ) if A x = λ B x for some λ . The investigation of properties of generalized eigenvectors is important for the applications. The values of vector or matrix inputs in practice are usually not exact numbers and they can be rather considered as values in some intervals. In this paper the properties of matrices and vectors with inexact (interval)...

-simplicity of interval max-min matrices

Ján Plavka, Štefan Berežný (2018)

Kybernetika

Similarity:

A matrix A is said to have 𝐗 -simple image eigenspace if any eigenvector x belonging to the interval 𝐗 = { x : x ̲ x x ¯ } containing a constant vector is the unique solution of the system A y = x in 𝐗 . The main result of this paper is an extension of 𝐗 -simplicity to interval max-min matrix 𝐀 = { A : A ̲ A A ¯ } distinguishing two possibilities, that at least one matrix or all matrices from a given interval have 𝐗 -simple image eigenspace. 𝐗 -simplicity of interval matrices in max-min algebra are studied and equivalent conditions for...

( 0 , 1 ) -matrices, discrepancy and preservers

LeRoy B. Beasley (2019)

Czechoslovak Mathematical Journal

Similarity:

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...

Row Hadamard majorization on 𝐌 m , n

Abbas Askarizadeh, Ali Armandnejad (2021)

Czechoslovak Mathematical Journal

Similarity:

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 real matrices. For A , B 𝐌 m , n , we say that A is row Hadamard majorized by B (denoted by A R H B ) if there exists an m × n row stochastic matrix R such that A = R B , where X Y is the Hadamard product (entrywise product) of matrices X , Y 𝐌 m , n . In this paper, we consider the concept of row Hadamard majorization as a relation on 𝐌 m , n and characterize the structure of all linear operators T : 𝐌 m , n 𝐌 m , n preserving...

On the combinatorial structure of 0 / 1 -matrices representing nonobtuse simplices

Jan Brandts, Abdullah Cihangir (2019)

Applications of Mathematics

Similarity:

A 0 / 1 -simplex is the convex hull of n + 1 affinely independent vertices of the unit n -cube I n . It is nonobtuse if none of its dihedral angles is obtuse, and acute if additionally none of them is right. Acute 0 / 1 -simplices in I n can be represented by 0 / 1 -matrices P of size n × n whose Gramians G = P P have an inverse that is strictly diagonally dominant, with negative off-diagonal entries. In this paper, we will prove that the positive part D of the transposed inverse P - of P is doubly stochastic and has the...

On row-sum majorization

Farzaneh Akbarzadeh, Ali Armandnejad (2019)

Czechoslovak Mathematical Journal

Similarity:

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 . ...

G-matrices, J -orthogonal matrices, and their sign patterns

Frank J. Hall, Miroslav Rozložník (2016)

Czechoslovak Mathematical Journal

Similarity:

A real matrix A is a G-matrix if A is nonsingular and there exist nonsingular diagonal matrices D 1 and D 2 such that A - T = D 1 A D 2 , where A - T denotes the transpose of the inverse of A . Denote by J = diag ( ± 1 ) a diagonal (signature) matrix, each of whose diagonal entries is + 1 or - 1 . A nonsingular real matrix Q is called J -orthogonal if Q T J Q = J . Many connections are established between these matrices. In particular, a matrix A is a G-matrix if and only if A is diagonally (with positive diagonals) equivalent to a column permutation...

Maps on upper triangular matrices preserving zero products

Roksana Słowik (2017)

Czechoslovak Mathematical Journal

Similarity:

Consider 𝒯 n ( F ) —the ring of all n × n upper triangular matrices defined over some field F . A map φ is called a zero product preserver on 𝒯 n ( F ) in both directions if for all x , y 𝒯 n ( F ) the condition x y = 0 is satisfied if and only if φ ( x ) φ ( y ) = 0 . In the present paper such maps are investigated. The full description of bijective zero product preservers is given. Namely, on the set of the matrices that are invertible, the map φ may act in any bijective way, whereas for the zero divisors and zero matrix one can write φ as a...

Cambrian fans

Nathan Reading, David E. Speyer (2009)

Journal of the European Mathematical Society

Similarity:

For a finite Coxeter group W and a Coxeter element c of W ; the c -Cambrian fan is a coarsening of the fan defined by the reflecting hyperplanes of W . Its maximal cones are naturally indexed by the c -sortable elements of W . The main result of this paper is that the known bijection cl c between c -sortable elements and c -clusters induces a combinatorial isomorphism of fans. In particular, the c -Cambrian fan is combinatorially isomorphic to the normal fan of the generalized associahedron for...

On a generalization of the Beiter Conjecture

Bartłomiej Bzdęga (2016)

Acta Arithmetica

Similarity:

We prove that for every ε > 0 and every nonnegative integer w there exist primes p 1 , . . . , p w such that for n = p 1 . . . p w the height of the cyclotomic polynomial Φ n is at least ( 1 - ε ) c w M n , where M n = i = 1 w - 2 p i 2 w - 1 - i - 1 and c w is a constant depending only on w; furthermore l i m w c w 2 - w 0 . 71 . In our construction we can have p i > h ( p 1 . . . p i - 1 ) for all i = 1,...,w and any function h: ℝ₊ → ℝ₊.

( m , r ) -central Riordan arrays and their applications

Sheng-Liang Yang, Yan-Xue Xu, Tian-Xiao He (2017)

Czechoslovak Mathematical Journal

Similarity:

For integers m > r 0 , Brietzke (2008) defined the ( m , r ) -central coefficients of an infinite lower triangular matrix G = ( d , h ) = ( d n , k ) n , k as d m n + r , ( m - 1 ) n + r , with n = 0 , 1 , 2 , , and the ( m , r ) -central coefficient triangle of G as G ( m , r ) = ( d m n + r , ( m - 1 ) n + k + r ) n , k . It is known that the ( m , r ) -central coefficient triangles of any Riordan array are also Riordan arrays. In this paper, for a Riordan array G = ( d , h ) with h ( 0 ) = 0 and d ( 0 ) , h ' ( 0 ) 0 , we obtain the generating function of its ( m , r ) -central coefficients and give an explicit representation for the ( m , r ) -central Riordan array G ( m , r ) in terms of the Riordan array G ....

Computing the greatest 𝐗 -eigenvector of a matrix in max-min algebra

Ján Plavka (2016)

Kybernetika

Similarity:

A vector x is said to be an eigenvector of a square max-min matrix A if A x = x . An eigenvector x of A is called the greatest 𝐗 -eigenvector of A if x 𝐗 = { x ; x ̲ x x ¯ } and y x for each eigenvector y 𝐗 . A max-min matrix A is called strongly 𝐗 -robust if the orbit x , A x , A 2 x , reaches the greatest 𝐗 -eigenvector with any starting vector of 𝐗 . We suggest an O ( n 3 ) algorithm for computing the greatest 𝐗 -eigenvector of A and study the strong 𝐗 -robustness. The necessary and sufficient conditions for strong 𝐗 -robustness are introduced...

On the unit group of a semisimple group algebra 𝔽 q S L ( 2 , 5 )

Rajendra K. Sharma, Gaurav Mittal (2022)

Mathematica Bohemica

Similarity:

We give the characterization of the unit group of 𝔽 q S L ( 2 , 5 ) , where 𝔽 q is a finite field with q = p k elements for prime p > 5 , and S L ( 2 , 5 ) denotes the special linear group of 2 × 2 matrices having determinant 1 over the cyclic group 5 .