Related papers: Characterization of matrices $B$ such that $(I,B,B…

We give a characterization of all matrices $A,B,C \in \mathbb{F}_{2}^{m \times m}$ which generate a $(0,m,3)$-net in base $2$ and a characterization of all matrices $B,C\in\mathbb{F}_{2}^{\mathbb{N}\times\mathbb{N}}$ which generate a…

The second author recently suggested to identify the generating matrices of a digital $(t,m,s)$-net over the finite field $F_q$ with an $s \times m$ matrix $C$ over $F_{q^m}$. More exactly, the entries of $C$ are determined by interpreting…

A banded matrix is a real square matrix where nonzero entries appear around the main diagonal. In this article, we consider linear complementarity properties of (variants) of banded matrices. Focusing on triangular matrices and the newly…

We explore the space of matrix-generated (0, m, 2)-nets and (0, 2)-sequences in base 2, also known as digital dyadic nets and sequences. In computer graphics, they are arguably leading the competition for use in rendering. We provide a…

We introduce a hybridization of digital sequences with uniformly distributed sequences in the domain of $b$-adic integers, $\mathbb Z_{b}, b\in\mathbb N\setminus\{1\}$, by using such sequences as input for generating matrices. The…

Consider the algebra M(n,F) of n x n matrices over an infinite field F of arbitrary characteristic. An identity for M(n,F) with forms is such a polynomial in n x n generic matrices and in \sigma_k(x), 0<k\leq n, coefficients in the…

We study distinct $(0,1)$ matrices $A$ and $B$, called \textit{Gram mates}, such that $AA^T=BB^T$ and $A^TA=B^TB$. We characterize Gram mates where one can be obtained from the other by changing signs of some positive singular values. We…

A symmetric positive semi-definite matrix A is called completely positive if there exists a matrix B with nonnegative entries such that A=BB^T. If B is such a matrix with a minimal number p of columns, then p is called the cp-rank of A. In…

Let K be an arbitrary field, and a,b,c,d be elements of K such that the polynomials t^2-at-b and t^2-ct-d are split in K[t]. Given a square matrix M with entries in K, we give necessary and sufficient conditions for the existence of two…

We give an easy algorithm which calculates the generating function of the cocharacter sequence of the T-ideal of the polynomial identities of the algebra of upper triangular matrices over a field of characteristic zero. Applying this…

We give a complete description of the varieties of associative algebras over a field of characteristic zero which satisfy a polynomial identity of third degree.

This paper studies zeros of networked linear systems with time-invariant interconnection topology. While the characterization of zeros is given for both heterogeneous and homogeneous networks, homogeneous networks are explored in greater…

Given any m-dimensional dilation matrix A with rational eigenvalues, we demonstrate the existence of a digit set D such that the attractor T(A,D) of the iterated function system generated by A and D is connected. We give an easily verified…

We study the dispersion of digital $(0,m,2)$-nets; i.e. the size of the largest axes-parallel box within such point sets. Digital nets are an important class of low-discrepancy point sets. We prove tight lower and upper bounds for certain…

Theorem 7 in Ref. [Linear Algebra Appl., 430, 1-6, (2009)] states sufficient conditions to determine whether a pair generates the algebra of 3x3 matrices over an algebraically closed field of characteristic zero. In that case, an explicit…

Inspired by Kontsevich's graphic orbifold Euler characteristic we define a virtual Euler characteristic for any finite set of isomorphism classes of matroids of rank $r$. Our main result provides a simple formula for the virtual Euler…

We study the differential identities of the algebra $M_k(F)$ of $k\times k$ matrices over a field $F$ of characteristic zero when its full Lie algebra of derivations, $L=\mbox{Der}(M_k(F))$, acts on it. We determine a set of 2 generators of…

In this article, we consider birational equivalence of exponential matrices. In characteristic zero, we give a birational classification of exponential matrices of size $n$-by-$n$ $(n \geq 2)$, which consists of two types. And in positive…

In this note, we consider matrices similar to $X$-form matrices, which are the matrices for which only the diagonal and the anti-diagonal elements can be different from zero. First, we give a characterization of these matrices using the…

It is known that every complex square matrix with nonnegative determinant is the product of positive semi-definite matrices. There are characterizations of matrices that require two or five positive semi-definite matrices in the product.…