Related papers: Commuting Magic Square Matrices

We show a matrix decomposition of flavor mass matrix for Dirac neutrinos $M$ by sum as $M=M'+M^0$ where $M'$ obeys the feature of the magic square and $M^0$ is three-zero texture. The favorable three-zero textures in the context of magic…

Let $n\geq2$ be a natural number. Let $M_n(\mathbb{K})$ be the ring of all $n \times n$ matrices over a field $\mathbb{K}$. Fix natural number $k$ satisfying $1<k\leq n$. Under a mild technical assumption over $\mathbb{K}$ we will show that…

We show that for all $k\ge 1$, there exists an integer $N(k)$ such that for all $n\ge N(k)$ the $k$-th order jet scheme over the commuting $n\times n$ matrix pairs scheme is reducible. At the other end of the spectrum, it is known that for…

A manifestly Lorentz-covariant calculus based on two matrix-coordinates and their associated derivatives is introduced. It allows formulating relativistic field theories in any even-dimensional spacetime. The construction extends a…

Let $\Gamma$ be a group of order $n^2$ and $SMS_{\Gamma}(n)=(a_{i,j})_{n\times n}$ be an $n\times n$ array whose entries are all distinct elements of $\Gamma$. If there exists an element $\mu\in\Gamma$ such that for every row $i$, there…

In order to find a suitable expression of an arbitrary square matrix over an arbitrary finite commutative ring, we prove that every such a matrix is always representable as a sum of a potent matrix and a nilpotent matrix of order at most…

We present an algorithm for computing a Smith form with multipliers of a regular matrix polynomial over a field. This algorithm differs from previous ones in that it computes a local Smith form for each irreducible factor in the determinant…

Polynomials commute under composition are referred to as commuting polynomials. In this paper, we study division properties for commuting polynomials with rational (and integer) coefficients. As a consequence, we show an algebraic…

The paper is devoted to the methods of solving simultaneous recurrences. Specifically, we discuss transformation of matrix recurrences to regular recurrences and propose a way of solving special matrix recurrences of order three by their…

This paper concerns the enumeration of simultaneous conjugacy classes of $k$-tuples of commuting matrices in the upper triangular group $GT_n(\mathbf F_q)$ and unitriangular group $UT_m(\mathbf F_q)$ over the finite field $\mathbf F_q$ of…

Ouroboros functions have shown some interesting properties when subjected to conventional operations. The aim of this paper is to continue our investigation and prove some additional properties of these functions. Using algebraic methods,…

The Jordan Canonical Form of a matrix is highly sensitive to perturbations, and its numerical computation remains a formidable challenge. This paper presents a regularization theory that establishes a well-posed least squares problem of…

In this short paper we have produced different kinds of upside down magic squares based on a palindromic day 11.02.2011. In this day appear only the algorisms 0, 1 and 2. Some of the magic squares are bimagic and some are palindromic. Magic…

In this note we mainly study the fine Jordan-Chevalley decomposition: a refinement of the classical Jordan-Chevalley decomposition of a matrix and we pay a particular attention to the field of the coefficients of the matrix. Moreover we…

Matrices over the dual numbers are considered. We propose an approach to classify these matrices up to similarity. Some preliminary results on the realization of this approach are obtained. In particular, we produce explicitly canonical…

Diaconis and Gamburd computed moments of secular coefficients in the CUE ensemble. We use the characteristic map to give a new combinatorial proof of their result. We also extend their computation to moments of traces of symmetric powers,…

Let $M_n$ denote the algebra of $n \times n$ complex matrices and let $\mathcal{A}\subseteq M_n$ be an arbitrary structural matrix algebra, i.e. a subalgebra of $M_n$ that contains all diagonal matrices. We consider injective maps $\phi :…

We consider a general concept of composition and decomposition of objects, and discuss a few natural properties one may expect from a reasonable choice thereof. It will be demonstrated how this leads to multiplication and co- multiplication…

The Jordan normal form for a matrix over an arbitrary field and the canonical form for a pair of matrices under contragredient equivalence are derived using Ptak's duality method.

We present a simple proof of the factorization of (complex) symmetric matrices into a product of a square matrix and its transpose, and discuss its application in establishing a uniqueness property of certain antilinear operators.