Related papers: Results about persymmetric matrices over F_2 and r…
The main purpose of this paper is to study the NP-complete subset-sum problem, not in the usual context of time-complexity-based classification of the algorithms (exponential/polynomial), but through a new kind of algorithmic classification…
In this paper, we give a survey of the known results concerning the tensor rank of the multiplication in finite extensions of finite fields, enriched with some not published recent results as well as analyzes enhancing the qualitative…
Some inequalities for positive linear maps on matrix algebras are given, especially asymmetric extensions of Kadison's inequality and several operator versions of Chebyshev's inequality. We also discuss well-known results around the matrix…
In this paper we investigate congruence relationships of particular finite generalized harmonic numbers sums. We suggest more transparent and simpler method to analyse these sums and present several additional results for certain special…
In this article we study two fundamental problems on exponential sums via randomization of frequencies with stochastic processes. These are the Hardy-Littlewood majorant problem, and $L^{2n}(\mathbb{T}), \ n\in \mathbb{N}$ norms of…
We consider the symmetric Toeplitz matrix completion problem, whose matrix under consideration possesses specific row and column structures. This problem, which has wide application in diverse areas, is well-known to be computationally…
We consider models of Bayesian inference of signals with vectorial components of finite dimensionality. We show that, under a proper perturbation, these models are replica symmetric in the sense that the overlap matrix concentrates. The…
The minimum rank problem for a (simple) graph $G$ is to determine the smallest possible rank over all real symmetric matrices whose $ij$th entry (for $i\neq j$) is nonzero whenever $\{i,j\}$ is an edge in $G$ and is zero otherwise. This…
This paper is about the study of F-transforms based on overlap and grouping maps, residual and co-residual implicator over complete lattice from both constructive and axiomatic approaches. Further, the duality, basic properties, and the…
We calculate the maximal dimension of linear spaces of symmetric and hermitian matrices with given high rank, generalizing a well-known result of Adams {\em et al.}
This article is dedicated to the following class of problems. Start with an $N\times N$ Hermitian matrix randomly picked from a matrix ensemble - the reference matrix. Applying a rank-$t$ perturbation to it, with $t$ taking the values $1\le…
The nonnegative integer rank of a matrix is a variant of the classical nonnegative rank, introduced in the 1980s, where factorizations are required to have integer entries. While computing nonnegative integer rank is generally very hard, we…
In this paper the sum of an orthogonal matrix and an outer product is studied, and a relation between the norms of the vectors forming the outer product and the singular values of the resulting matrix is presented. The main result may be…
We survey some principal results and open problems related to colorings of geometric and algebraic objects endowed with symmetries, concentrating the exposition on the maximal symmetry numbers of such objects.
Inequalities for exponential sums are studied. Our results improve an old result of G. Halasz and a recent result of G. Kos. We prove several other essentially sharp related results in this paper.
The problem of approximate joint diagonalization of a collection of matrices arises in a number of diverse engineering and signal processing problems. This problem is usually cast as an optimization problem, and it is the main goal of this…
We review some convexity inequalities for Hermitian matrices an add one more to the list.
The paper explores the concept of the rank of a bicomplex matrix, delving into four distinct types of ranks and investigating conditions under which these ranks are equivalent. It also defines and analyzes the concept of idempotent row…
We consider higher-rank versions of the standard numerical range for matrices. A central motivation for this investigation comes from quantum error correction. We develop the basic structure theory for the higher-rank numerical ranges, and…
This work studies the distribution of the nonsymmetric matrix $\mathbf{E}^{-1}\mathbf{H}$. This random product is of fundamental interest under the general multivariate linear hypothesis setting. Specifically when $\mathbf{H}$ and…