相关论文: New results on the parametrisation of complex Hada…
A partial Hadamard matrix is a matrix $H\in M_{M\times N}(\mathbb T)$ whose rows are pairwise orthogonal. We associate to each such $H$ a certain quantum semigroup $G$ of quantum partial permutations of $\{1,...,M\}$ and study the…
Let $n$ be the order of a (quaternary) Hadamard matrix. It is shown that the existence of a projective plane of order $n$ is equivalent to the existence of a balancedly multi-splittable (quaternary) Hadamard matrix of order $n^2$.
In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. The algorithm uses a variable stepsize which is updated at each iteration and based on some previous…
These notes develop aspects of perturbation theory of matrices related to so-called diagonalisation schemes. Primary focus is on constructive tools to derive asymptotic expansions for small/large parameters of eigenvalues and…
We introduce a new matroid width parameter based on the operation of matroid amalgamation, which we call amalgam-width. The parameter is linearly related to branch-width on finitely representable matroids (which is not possible for…
This dissertation presents new results on three different themes all related to matroid polytopes. First we investigate properties of Ehrhart polynomials of matroid polytopes, independence matroid polytopes, and polymatroids. We prove that…
A new, two-parameter, nonaffine family of complex Hadamard matrices of order 6 is reported. It interpolates between the two Fourier families, and contains as one-parameter subfamilies the Dita family, a symmetric family and an almost (up to…
In this paper, we consider the stationary measure of the Hadamard walk on the one-dimensional integer lattice. Here all the stationary measures given by solving the eigenvalue problem are completely determined via the transfer matrix…
A notable difference between the ordinary and Hadamard products is that the Hadamard product of two singular positive semidefinite matrices can be nonsingular, and one of the factors can even be indefinite. We present an eigenvalue lower…
A trade in a complex Hadamard matrix is a set of entries which can be changed to obtain a different complex Hadamard matrix. We show that in a real Hadamard matrix of order $n$ all trades contain at least $n$ entries. We call a trade…
Provided that a cohomological model for $G$ is known, we describe a method for constructing a basis for $n$-cocycles over $G$, from which the whole set of $n$-dimensional $n$-cocyclic matrices over $G$ may be straightforwardly calculated.…
We computationally resolve an open problem concerning the expressibility of $4 \times 4$ full-rank matrices as Hadamard products of two rank-2 matrices. Through exhaustive search over $\mathbb{F}_2$, we identify 5,304 counterexamples among…
Convolutions or Hadamard products of analytic functions is a well explored area of research and many nice results are available in literature. On the other hand, very little is known in general about the convolutions of univalent harmonic…
In this survey paper we study parametric versions of writing a matrix in $SL_n (\mathbb{C})$ as a product of lower and upper unitriangular matrices in interchanging order as well as generalizations to other classical groups. We give an…
In this paper, we study approximate Hadamard matrices, that is, well-conditioned $n\times n$ matrices with all entries in $\{\pm1\}$. We show that the smallest-possible condition number goes to $1$ as $n\to\infty$, and we identify some…
We introduce the parametric matroid one-interdiction problem. Given a matroid, each element of its ground set is associated with a weight that depends linearly on a real parameter from a given parameter interval. The goal is to find, for…
The geometric phase is usually treated as a quantity modulo 2\pi, a convention carried over from early work on the subject. The results of a series of optical interference experiments involving polarization of light, done by the present…
In this paper we introduce modular symmetric designs and use them to study the existence of Hadamard matrices modulo 5. We prove that there exist 5-modular Hadamard matrices of order n if and only if n != 3, 7 (mod 10) or n != 6, 11. In…
Balancedly splittable Hadamard matrices are introduced and studied. A connection is made to the Hadamard diagonalizable strongly regular graphs, maximal equiangular lines set, and unbiased Hadamard matrices. Several construction methods are…
Many rationally parametrized elliptic modular equations are derived. Each comes from a family of elliptic curves attached to a genus-zero congruence subgroup $\Gamma_0(N)$, as an algebraic transformation of elliptic curve periods,…