相关论文: Three families of matrices

We study the boundedness of families of algebraic flat connections with bounded irregularity. As an application, we study the boundedness of families of holonomic $D$-modules with dominated characteristic cycles.

We systematically study how properties of abstract operator systems help classifying linear matrix inequality definitions of sets. Our main focus is on polyhedral cones, the 3-dimensional Lorentz cone, where we can completely describe all…

Multiplicative matrix semigroups with constant spectral radius (c.s.r.) are studied and applied to several problems of algebra, combinatorics, functional equations, and dynamical systems. We show that all such semigroups are characterized…

An algebraic investigation on bicomplex numbers is carried out here. Particularly matrices and linear maps defined on them are discussed. A new kind of cartesian product, referred to as an idempotent product, is introduced and studied. The…

This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…

We say that two elements of a group or semigroup are $\Bbbk$-linear conjugates if their images under any linear representation over $\Bbbk$ are conjugate matrices. In this paper we characterize $\Bbbk$-linear conjugacy for finite semigroups…

We analyze when an arbitrary matrix pencil is equivalent to a dissipative Hamiltonian pencil and show that this heavily restricts the spectral properties. In order to relax the spectral properties, we introduce matrix pencils with…

The family of cycle completable graphs has several cryptomorphic descriptions, the equivalence of which has heretofore been proven by a laborious implication-cycle that detours through a motivating matrix completion problem. We give a…

We survey a variety of results about partially isometric matrices. We focus primarily on results that are distinctly finite-dimensional. For example, we cover a recent solution to the similarity problem for partial isometries. We also…

Six non-affine 3-parameter families of complex Hadamard matrices of order 8 are presented. These families contain Hadamard matrices that are not equivalent to any previously known Hadamard matrices in the literature. Each family arises from…

We characterize all real matrix semigroups satisfying a mild boundedness assumption, without assuming continuity. Besides the continuous solutions of the semigroup functional equation, we give a description of solutions arising from…

We study the problem when every matrix over a division ring is representable as either the product of traceless matrices or the product of semi-traceless matrices, and also give some applications of such decompositions. Specifically, we…

We define and investigate a new three-parameter family of graphs that further generalizes the Fibonacci and metallic cubes. Namely, the number of vertices in this family of graphs satisfies Horadam recurrence, a linear recurrence of second…

Metric spaces satisfying properties stronger than completeness and weaker than compactness have been studied by many authors over the years. One such significant family is that of cofinally complete metric spaces. We discuss the…

Positive semidefinite Hermitian matrices that are not fully specified can be completed provided their underlying graph is chordal. If the matrix is positive definite the completion can be uniquely characterized as the matrix that maximizes…

Positive semidefinite matrices partitioned into a small number of Hermitian blocks have a remarkable property. Such a matrix may be written in a simple way from the sum of its diagonal blocks

A new matrix product, called the semi-tensor product (STP), is briefly reviewed. The STP extends the classical matrix product to two arbitrary matrices. Under STP the set of matrices becomes a monoid (semi-group with identity). Some related…

Quantum families of maps between quantum spaces are defined and studied. We prove that quantum semigroup (and sometimes quantum group) structures arise naturally on such objects out of more fundamental properties. As particular cases we…

The task of analytically diagonalizing a tridiagonal matrix can be considerably simplified when a part of the matrix is uniform. Such quasi-uniform matrices occur in several physical contexts, both classical and quantum, where…

We analyze the complex analytic properties of Classical (tree-level) S-matrices for four scalar particles with s-t crossing symmetry, involving an infinite number of exchanges. Under suitable analytic conditions, we demonstrate that such…