Related papers: Some bounds for determinants of relatively $D$-sta…
Let $A$ be a set in a prime field $\mathbb{F}_p$. In this paper, we prove that $d\times d$ matrices with entries in $A$ determine almost $|A|^{3+\frac{1}{45}}$ distinct determinants and almost $|A|^{2-\frac{1}{6}}$ distinct permanents when…
This note explores the extension of D-stability to non-square matrices, applicable to distributed/decentralized controllability analysis. We first present a definition of D-stability for non-square matrices, directly extending from square…
We study the maximum absolute value of the determinant of matrices with entries in the set of $\ell$-th roots of unity; this is a generalization of $D$-optimal designs and Hadamard's maximal determinant problem, which involves $\pm 1$…
This paper introduces and investigates a novel class of skew-regular Quaternary Hadamard matrices. For every odd prime power $p$, we establish the existence of these matrices for all orders $1+p^2$, each characterized by a constant row sum…
We prove stability of logarithmic tangent sheaves of singular hypersurfaces D of the projective space with constraints on the dimension and degree of the singularities of D. As main application, we prove that determinants and symmetric…
In this paper, we obtain some new matrix inequalities involving Hadamard product. Also some Hadamard product inequalities for accretive matrices involving the matrix means, positive unital linear maps and matrix concave functions are…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
We provide a systematic approach to stable central limit theorems for d-dimensional martingale difference arrays and martingale difference sequences. The conditions imposed are straightforward extensions of the univariate case.
In this paper we shed more light on determinants of interval matrices. Computing the exact bounds on a determinant of an interval matrix is an NP-hard problem. Therefore, attention is first paid to approximations. NP-hardness of both…
Two matrices with elements taken from the set {-1,1} are Hadamard equivalent if one can be converted into the other by a sequence of permutations of rows and columns, and negations of rows and columns. In this paper we summarize what is…
In this framework, the extremal case corresponds to the tightest nontrivial relaxation in this hierarchy, in which every proper principal submatrix is constrained to be positive semidefinite, while the global positive semidefiniteness…
We propose a modified condition of consistency on cubic lattices for some special classes of two-dimensional discrete equations and prove that the discrete nonlinear equations defined by determinants of matrices of orders N > 2 are…
This paper gives a necessary and sufficient condition for robust D-stability of Polytopic Polynomial Matrices. Edge theorem is extended to multi-input-multi-output case.
We develop here the method for obtaining approximate stability boundaries in the space of parameters for systems with parametric excitation. The monodromy (Floquet) matrix of linearized system is found by averaging method. For system with 2…
We extend the definition of $n$-dimensional difference equations to complex order $\alpha\in \mathbb{C} $. We investigate the stability of linear systems defined by an $n$-dimensional matrix $A$ and derive conditions for the stability of…
We find explicit stability bounds for exponential Riesz bases on domains of R^d. Our results generalize Kadec theorem and other stability theorems in the literature.
Let F be an N x N complex matrix whose jth column is the vector f_j in C^N. Let |f_j|^2 denote the sum of the absolute squares of the entries of f_j. Hadamard's inequality for determinants states that |\det(F)| <= \prod_{j=1}^N|f_j|. Here…
This paper investigates the robustness of exponential stability of a class of switched systems described by linear functional differential equations under arbitrary switching. We will measure the stability robustness of such a system,…
New necessary and sufficient conditions are proposed for the stability investigation of dynamical systems using the flow and the divergence of the phase vector velocity. The obtained conditions generalize the well-known results of V.P.…
The paper presents methods of eigenvalue localisation of regular matrix polynomials, in particular, stability of matrix polynomials is investigated. For this aim a stronger notion of hyperstability is introduced and widely discussed. Matrix…