Related papers: Submatrices of Hadamard matrices: complementation …

Almost-commuting matrices with respect to the normalized Hilbert-Schmidt norm are considered. Normal almost commuting matrices are proved to be near commuting.

For a linear complementarity problem, we present a relaxaiton accelerated two-sweep matrix splitting iteration method. The convergence analysis illustrates that the proposed method converges to the exact solution of the linear…

Base on some simple facts of Hadamard product, characterizations of positive definite preserving linear transformations on real symmetric matrix spaces with an additional assumption "$\ra T(E_{ii})=1, i=1,2,..., n$" or "$T(A)>0\to A> 0$",…

Let H be a Hopf algebra. By definition a modular crossed H-module is a vector space M on which H acts and coacts in a compatible way. To every modular crossed H-module M we associate a cyclic object Z(H,M). The cyclic homology of Z(H,M)…

First we give an overview of the known supplementary difference sets (SDS) (A_i), i=1..4, with parameters (n;k_i;d), where k_i=|A_i| and each A_i is either symmetric or skew and k_1 + ... + k_4 = n + d. Five new Williamson matrices over the…

We study a class of almost diagonal matrices compatible with the mixed-norm $\alpha$-modulation spaces $M_{\vec{p},q}^{s,\alpha}(\mathbb{R}^n)$, $\alpha\in [0,1]$, introduced recently by Cleanthous and Georgiadis [Trans.\ Amer.\ Math.\…

The purpose of this paper is to introduce new parametric families of complex Hadamard matrices in two different ways. First, we prove that every real Hadamard matrix of order N>=4 admits an affine orbit. This settles a recent open problem…

If $N=2^k > 8$ then there exist exactly $[(k-1)/2]$ pairwise nonequivalent $Z_4$-linear Hadamard $(N,2N,N/2)$-codes and $[(k+1)/2]$ pairwise nonequivalent $Z_4$-linear extended perfect $(N,2^N/2N,4)$-codes. A recurrent construction of…

Let A be an n by d matrix having full rank n. An orthogonal dual A^{\perp} of A is a (d-n) by d matrix of rank (d-n) such that every row of A^{\perp} is orthogonal (under the usual dot product) to every row of A. We define the orthogonal…

We provide convergent hierarchies for the cone C of copositive matrices and its dual, the cone of completely positive matrices. In both cases the corresponding hierarchy consists of nested spectrahedra and provide outer (resp. inner)…

We prove that the algebraic set of pairs of matrices with a diagonal commutator over a field of positive prime characteristic, its irreducible components, and their intersection are $F$-pure when the size of matrices is equal to 3.…

A collection of complex sequences of length v is complementary if the sum of their periodic autocorrelation function values at all non-zero shifts is constant. For a complex sequence A=[a_0,a_1,...,a_{v-1}] of length v=dm we define the…

Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating…

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…

In this paper we present new Hadamard matrices and related combinatorial structures. In particular, it is constructed 5202 inequivalent Hadamard matrices of order 36 as well as 180538 Hadamard symmetric designs with 35 points in addition to…

We give an explicit construction, based on Hadamard matrices, for an infinite series of floor{sqrt{d}/2}-neighborly centrally symmetric d-dimensional polytopes with 4d vertices. This appears to be the best explicit version yet of a recent…

A module $M$ is called H-supplemented if for every submodule $A$ of $M$ there is a direct summand $A'$ of $M$ such that $A+X=M$ holds if and only if $A'+X=M$ for any submodule $X$ of $M$. (Equivalently, for each $X\leq M$, there exists a…

Two trace formulas for the spectra of arbitrary Hermitian matrices are derived by transforming the given Hermitian matrix $H$ to a unitary analogue. In the first type the unitary matrix is $e^{i(\lambda\II - H)}$ where $\lambda$ is the…

Consider a unital C*-algebra A, a von Neumann algebra M, a unital sub-C*-algebra C of A and a unital *-homomorphism $\pi$ from C to M. Let u: A --> M be a decomposable map (i.e. a linear combination of completely positive maps) which is a…

Given matrices $A$ and $B$ such that $B=f(A)$, where $f(z)$ is a holomorphic function, we analyze the relation between the singular values of the off-diagonal submatrices of $A$ and $B$. We provide family of bounds which depend on the…