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( 0 , 1 ) -matrices, discrepancy and preservers

LeRoy B. Beasley (2019)

Czechoslovak Mathematical Journal

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...

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

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

Czechoslovak Mathematical Journal

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 . Meanwhile, the...

𝒟 n , r is not potentially nilpotent for n 4 r - 2

Yan Ling Shao, Yubin Gao, Wei Gao (2016)

Czechoslovak Mathematical Journal

An n × n sign pattern 𝒜 is said to be potentially nilpotent if there exists a nilpotent real matrix B with the same sign pattern as 𝒜 . Let 𝒟 n , r be an n × n sign pattern with 2 r n such that the superdiagonal and the ( n , n ) entries are positive, the ( i , 1 ) ( i = 1 ...

± sign pattern matrices that allow orthogonality

Yan Ling Shao, Liang Sun, Yubin Gao (2006)

Czechoslovak Mathematical Journal

A sign pattern A is a ± sign pattern if A has no zero entries. A allows orthogonality if there exists a real orthogonal matrix B whose sign pattern equals A . Some sufficient conditions are given for a sign pattern matrix to allow orthogonality, and a complete characterization is given for ± sign patterns with n - 1 N - ( A ) n + 1 to allow orthogonality.

517.98

A.M. Вершик (1984)

Zapiski naucnych seminarov Leningradskogo

A bound for the rank-one transient of inhomogeneous matrix products in special case

Arthur Kennedy-Cochran-Patrick, Sergeĭ Sergeev, Štefan Berežný (2019)

Kybernetika

We consider inhomogeneous matrix products over max-plus algebra, where the matrices in the product satisfy certain assumptions under which the matrix products of sufficient length are rank-one, as it was shown in [6] (Shue, Anderson, Dey 1998). We establish a bound on the transient after which any product of matrices whose length exceeds that bound becomes rank-one.

A boundary-value problem for linear PDAEs

Wiesław Marszałek, Zdzisław Trzaska (2002)

International Journal of Applied Mathematics and Computer Science

We analyze a boundary-value problem for linear partial differential algebraic equations, or PDAEs, by using the method of the separation of variables. The analysis is based on the Kronecker-Weierstrass form of the matrix pencil[A,-λ_n B]. A new theorem is proved and two illustrative examples are given.

A Brauer’s theorem and related results

Rafael Bru, Rafael Cantó, Ricardo Soto, Ana Urbano (2012)

Open Mathematics

Given a square matrix A, a Brauer’s theorem [Brauer A., Limits for the characteristic roots of a matrix. IV. Applications to stochastic matrices, Duke Math. J., 1952, 19(1), 75–91] shows how to modify one single eigenvalue of A via a rank-one perturbation without changing any of the remaining eigenvalues. Older and newer results can be considered in the framework of the above theorem. In this paper, we present its application to stabilization of control systems, including the case when the system...

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