Related papers: On a matrix equality involving partial transpositi…

Let $\bold G$ be a reductive algebraic group defined over $\Q$, and let $\Gamma$ be an arithmetic subgroup of $\bold G(\Q)$. Let $X$ be the symmetric space for $\bold G(\R)$, and assume $X$ is contractible. Then the cohomology (mod torsion)…

We define and study fractional versions of the well-known Gamma subordinator $\Gamma :=\{\Gamma (t),$ $t\geq 0\},$ which are obtained by time-changing $% \Gamma $ by means of an independent stable subordinator or its inverse. Their…

We calculate the branching ratios of $B_{s,d}\to \gamma \gamma$ decay in the sequential fourth generation model. We find that the theoretical values of the branching ratios, ${\rm BR}(B_{s}\to\gamma\gamma)$, including the contributions of…

It is well-known that $AB$ and $BA$ are similar when $A$ and $B$ are complex square Hermitian matrices. In this note we answer a question of F. Zhang by demonstrating that similarity can fail if $A$ is Hermitian and $B$ is normal. Perhaps…

We prove that a C$^*$-algebra $A$ has uniform property $\Gamma$ if the set of extremal tracial states, $\partial_e T(A)$, is a non-empty compact space of finite covering dimension and for each $\tau \in \partial_e T(A)$, the von Neumann…

A well-known fact in linear algebra is that $A^T A$ is always positive semi-definite for any real matrix $A$. We consider a generalization of this fact via the following decision problem. Given a symbolic product of length $k$, consisting…

Some recent papers formulated sufficient conditions for the decomposition of matrix variances. A statement was that if we have one or two observables, then the decomposition is possible. In this paper we consider an arbitrary finite set of…

We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance…

The general expression with the physical significance and positive definite condition of the eigenvalues of $4\times 4$ Hermitian and trace-one matrix are obtained. This implies that the eigenvalue problem of the $4\times 4$ density matrix…

We present matrices as graded BiHom-algebras and consider various characteristics of their decompositions. Specifically, we introduce a notion of connection in the support of the grading and use it to construct a family of canonical graded…

A status report on the theory and phenomenology of rare radiative $B$ decays in the standard model is presented with emphasis on the measured decays $B \to X_s \gamma$ and $B \to K^* \gamma$. Standard model is in agreement with experiments…

In this paper we give alternate proofs of some well-known matrix inequalities. In particular, we show that under certain conditions the inequality holds \begin{align}\sum \limits_{\lambda_i\in \mathrm{Spec}(ab^{T})}\mathrm{min}\{\log…

Let $\Gamma$ be a $Q$-polynomial distance-regular graph with diameter at least $3$. Terwilliger (1993) implicitly showed that there exists a polynomial, say $T(\lambda)\in \mathbb{C}[\lambda]$, of degree $4$ depending only on the…

We consider a class of graphs subject to certain restrictions, including the finiteness of diameters. Any surjective mapping $\phi:\Gamma\to\Gamma'$ between graphs from this class is shown to be an isomorphism provided that the following…

Let $\Gamma$ denote a distance-regular graph with classical parameters $(D,b,\alpha,\beta)$ and $b\not=1$, $\alpha=b-1$. The condition on $\alpha$ implies that $\Gamma$ is formally self-dual. For $b=q^2$ we use the adjacency matrix and dual…

Given a real matrix A with n columns, the problem is to approximate the Gram product AA^T by c << n weighted outer products of columns of A. Necessary and sufficient conditions for the exact computation of AA^T (in exact arithmetic) from c…

Gardner conjectured that if two bounded measurable sets $A,B \subset \mathbb{R}^n$ are equidecomposable by a set of isometries $\Gamma$ generating an amenable group then $A$ and $B$ admit a measurable equidecomposition by all isometries.…

In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…

We investigate the distillability problem in quantum information in $\bbC^d\ox\bbC^d$. A special case of the problem has been reduced to proving a matrix inequality when $d=4$. We investigate the inequality for two families of non-normal…

Matrix Completion is the problem of recovering an unknown real-valued low-rank matrix from a subsample of its entries. Important recent results show that the problem can be solved efficiently under the assumption that the unknown matrix is…