Related papers: On Symmetric Norm Inequalities And Hermitian Block…
This article is concerned with perfect isometries between blocks of finite groups. Generalizing a method of Enguehard to show that any two p-blocks of (possibly different) symmetric groups with the same weight are perfectly isometric, we…
The paper gives a thorough introduction to spectra of digraphs via its Hermitian adjacency matrix. This matrix is indexed by the vertices of the digraph, and the entry corresponding to an arc from $x$ to $y$ is equal to the complex unity…
Block coordinate methods have been extensively studied for minimization problems, where they come with significant complexity improvements whenever the considered problems are compatible with block decomposition and, moreover, block…
This paper is concentrated on the classification of permutation matrix with the permutation similarity relation, mainly about the canonical form of a permutational similar equivalence class, the cycle matrix decomposition of a permutation…
Block coherence of matrices plays an important role in analyzing the performance of block compressed sensing recovery algorithms (Bajwa and Mixon, 2012). In this paper, we characterize two block coherence metrics: worst-case and average…
The purpose of the present work is to introduce the concept of relative EP matrix of a rectangular matrix relative to a partial isometry (or, in short, $T$-EP matrix) hitherto unknown. We extend various basic results on EP matrices and we…
This paper studies systems of linear difference equations on the lattice $\Z^n$ that are invariant under a finite group of symmetries, and shows that there exist solutions to such systems that are also invariant under this group of…
We provide a detailed description of the maps associated with spectral interlacing, for rank one perturbations and bordering of symmetric and Hermitian matrices. The arguments rely on standard techniques of nonlinear analysis.
We introduce a class of $G$-invariant connections on a homogeneous principal bundle $Q$ over a hermitian symmetric space $M=G/K$. The parameter space carries the structure of normal variety and has a canonical anti-holomorphic involution.…
In this paper we study how certain symmetries of convex bodies affect their geometric properties. In particular, we consider the impact of symmetries generated by the block diagonal subgroup of orthogonal transformations, generalizing…
The least square solution of minimum norm of a rectangular linear system of equations can be found out iteratively by using matrix splittings. However, the convergence of such an iteration scheme arising out of a matrix splitting is…
Maximum Hermitian rank metric codes were introduced by Schmidt in 2018 and in this paper we propose both interpolation-based encoding and decoding algorithms for this family of codes when the length and the minimum distance of the code are…
Given some non-Archimedean field $\mathbb{K}$ and some $\mathbb{K}$-linear space $X$, the usual way to define a norm over $X$ involves the {\em ultrametric inequality} $\|x+y\|\leq\max\{\|x\|,\|y\|\}$. In this note we will try to analyse…
Let $D$ denote a positive integer and let $Q_D$ denote the graph of the $D$-dimensional hypercube. Let $X$ denote the vertex set of $Q_D$ and let $A \in \MX$ denote the adjacency matrix of $Q_D$. A matrix $B \in \MX$ is called $A$-{\em…
Conformal block divisors in type A on $\bar{M}_{0,{n}}$ are shown to satisfy new symmetries when levels and ranks are interchanged in non-standard ways. A connection with the quantum cohomology of Grassmannians reveals that these divisors…
This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…
We present several matrix and operator inequalities of Hermite-Hadamard type. We first establish a majorization version for monotone convex functions on matrices. We then utilize the Mond-Pecaric method to get an operator version for convex…
A complete geometric classification of symmetries of autonomous Hamiltonian mechanical systems is established; explaining how to obtain their associated conserved quantities in all cases. In particular, first we review well-known results…
We define Boolean algebras in the linear context and study its symmetric powers. We give explicit formulae for products in symmetric Boolean algebras of various dimensions. We formulate symmetric forms of the inclusion-exclusion principle.
In this paper we outline a setup for Homological Mirror Symmetry for manifolds of general type. Both Physics and Categorical perspectives are considered.