Some counterexamples related to sectorial matrices and matrix phases

Some Constructions Related to Rees Matrix Rings

Simple rings with a one-sided minimal ideal may be represented as Rees matrix rings, and conversely. The latter are defined as I ×Λ matrices over a division ring with only a finite number of nonzero entries with certain addition and multiplication. For Rees matrix rings we construct here their isomorphisms, their translational hulls and isomorphisms of the translational hulls, all this in terms...

Theorems and counterexamples on structured matrices

Some New Matrix Formulas Related to Hermite Matrix Polynomials Theory

In this paper an integral representation for the Hermite matrix polynomials is given. By means of the exact computation of certain matrix integrals and the integral representation of Hermite matrix polynomials, a formula for the generating function of the product of Her-mite matrix polynomials is obtained. Both the integral representation of the Hermite matrix polynomials and the formula for th...

Some Formulas for Invariant Phases of Unitary Matrices by Jarlskog

CP violation is expected in the standard model of particle physics with three or more families [1], [2]. Therefore it is an important problem that what is the measure of CP violation with such families which is invariant under the action of phase factors. To construct invariants for matrix action, the determinant is a useful tool. In the previous paper [3], C. Jarlskog succeeded to define invar...

The Distance Matrices of Some Graphs Related to Wheel Graphs

A simple graph G = (V, E) consists of V, a nonempty set of vertices, and E, a set of unordered pairs of distinct elements of V called edges. All graphs considered here are simple and connected. LetG be a simple connected graph with vertex set V(G) and edge set E(G).The distance between two vertices u, V ∈ V(G) is denoted by d uV and is defined as the length of the shortest path between u and V ...