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About 10,000 papers for “Matrix representation”

The Primitive Matrix Representation and Symmetric Matrix Representation of Finite Fields

<p>Yuying Ou, Wenbin Zhang</p> · Academic Journal of Mathematical Sciences · 2024

In this paper, we consider the matrix representations of the finite field, and show some conclusions of the primitive matrix representation of the finite field on the ground field by using the properties of the cyclotomic polynomial. We obtain the symmetric matrix representation of the finite field F<sub>q</sub> with characteristic 2 by constructing the symmetric matrix, and get the relationship between the symmetric matrix representation and the primitive matrix representation of the finite field <span style="text-wrap: wrap;">F</span><sub style="text-wrap: wrap;">q</sub>.

Cited by 0Open access

Matrix representation of disemigraphs

Sampathkumar, J. E., Pushpalatha, L. · MyPrints@UOM (Mysore University Library) · 2013

A disemigraph can be uniquely represented by a matrix and a characterization of such a matrix is obtained.

Cited by 0

Optics using matrix representation

<vcard>BEGIN:vCard\VERSION:3.0\FN:Amy Lytle\ORG:Franklin &amp; Marshall College\ADR;TYPE=WORK,POSTAL,PARCEL:;;;;;;;US\END:vCard</vcard> · The Physics Video Demonstration Database (Cornell University)

Cited by 0

Matrix Representation of Groups

P. F. Bernath · 2025

Abstract This chapter begins with a mathematical review of matrices and vectors. The representation of symmetry operators by matrices is presented. The effect of symmetry operators on basis functions is demonstrated. Matrix representations of groups are defined, and equivalent, reducible and irreducible representations given. The Great Orthogonality Theorem for the matrix representation of groups is introduced. Characters of matrices are presented along with character tables for the main point groups.

Cited by 0

Matrix representation of simple halfrings

H. E. Stone · Transactions of the American Mathematical Society · 1977

The structure of halfrings which are strong direct sums of minimal subtractive right ideals is studied. A class of right simple hemirings which contains both division hemirings and differential subsemirings of division rings is introduced and studied extensively as a tool in this investigation. A matrix representation is obtained for a class of halfrings which properly includes differential subsemirings of simple Artinian rings.

Cited by 5

A Matrix of Material Representation.

Hengfeng Zuo, Mark Jones, Tony Hope · Proceedings of DRS · 2004

The sensory properties of materials such as colour, texture, sound, smell, etc and people’s perceptual responses to them are very important information for designers to consider when selecting or combining materials for a manufactured product. Based on theoretical, experimental and computer programming methods, this research has established a framework of a database referred to as ‘Matrix of Material Representation’. The Matrix is a visual narrative model that systematically contains the holistic information about the factors involved in the human perception of materials and illustrates the interrelationship between these factors. Currently, the detailed information about material texture perception has been integrated into the Matrix, which includes a series of material texture perception maps. The Matrix is expected to provide guidance and a reference point to enable design practitioners to make intelligent judgements in selecting and combining different materials in order to match human sensory adaptation, aesthetical and perceptual expectation. The Matrix is seen as evolutionary and therefore has been designed to allow further research data to be integrated at future points. The paper presented here will give a detailed introduction to the Matrix and its dynamic development.

Cited by 7Open access

Matrix Representation on Quaternion Algebra

Gülay Koru Yücekaya · DergiPark (Istanbul University) · 2016

The quaternions, denoted by H, were first defined by W.R. Hamilton in 1843 as an extension of the four dimensions complex numbers. Hamilton has included a new multiplication process to vector algebra by defining quaternions for two vectors where the division process is available. In this paper, basic operations on H/Zp quaternion and the matrix form which belong to H/Zp quaternion algebra are given

Cited by 0

Matrix Representation of Special Relativity

2007

I compare the matrix representation of the basic statements of Special Relativity with the conventional vector space representation. It is shown, that the matrix form reproduces all equations in a very concise and elegant form, namely: Maxwell equations, Lorentz-force, energy-momentum tensor, Dirac-equation and Lagrangians. The matrix representation requires fewer assumptions, uses fewer parameters and may lead to new insights into physical reality. A new result is a matrix form of Dirac’s equation. It can explain the non-existence of right-handed neutrinos and can be generalized to include a new variant of Yang-Mills gauge fields, which possibly express unified electro-weak interactions.

Cited by 0

Matrix Representation of Simple Halfrings

H. E. Stone · Transactions of the American Mathematical Society · 1977

The structure of halfrings which are strong direct sums of minimal subtractive right ideals is studied.A class of right simple hemirings which contains both division hemirings and differential subsemirings of division rings is introduced and studied extensively as a tool in this investigation.A matrix representation is obtained for a class of halfrings which properly includes differential subsemirings of simple Artinian rings.1. Introduction.A semiring is a triple (H, +, ) such that (H, + ) is a semigroup with identity 0, (H, ) is semigroup with zero 0, and multiplication distributes over addition.If the addition is commutative, H is called a hemiring.A subsemiring S of a hemiring H is differential in HifVhEH 3s, t G S with s + h = t.A halfring is a hemiring H which is differential in some ring H, which is then uniquely determined.This paper continues the point of view of [9], and terminology introduced there will be extended without comment to hemirings generally.A hemiring is [right, left] simple if it has no nontrivial subtractive [right, left] ideals.It is [right, left] ideal-free if it has no nontrivial [right, left] ideals.A division semiring is a semiring with 1 = 0 all of whose nonzero elements have multiplicative inverse.It is clear that division hemirings may be characterized among nonzero hemirings as those which are right and left ideal-free, and among hemirings with identity as those which are right ideal-free.Grillet and Grillet [4], [5] have recently studied ideal-free and semisimple semirings very successfully using the techniques of semigroup theory.Earlier, Bourne [1], Bourne and Zassenhaus [2], [3], Steinfeld [8], and Wiegant [10] had studied semirings which are direct sums of minimal right ideals.The culmination of that study is an analogue of the Wedderburn theorem which may be paraphrased as follows:An ideal-free semiring with identity which is a strong direct sum of finitely many minimal right ideals is isomorphic to a full semiring of matrices over a division semiring.

Cited by 1Open access

A Matrix of Material Representation

Hengfeng Zuoa, Mark Jonesb, Tony Hopea · 2015

The sensory properties of materials such as colour, texture, sound, smell, etc and people’s perceptual responses to them are very important information for designers to consider when selecting or combining materials for a manufactured product. Based on theoretical, experimental and computer programming methods, this research has established a framework of a database referred to as ‘Matrix of Material Representation’. The Matrix is a visual narrative model that systematically contains the holistic information about the factors involved in the human perception of materials and illustrates the interrelationship between these factors. Currently, the detailed information about material texture perception has been integrated into the Matrix, which includes a series of material texture perception maps. The Matrix is expected to provide guidance and a reference point to enable design practitioners to make intelligent judgements in selecting and combining different materials in order to match human sensory adaptation, aesthetical and perceptual expectation. The Matrix is seen as evolutionary and therefore has been designed to allow further research data to be integrated at future points. The paper presented here will give a detailed introduction to the Matrix and its dynamic development. Key words: Matrix/database, materials selection, sensory properties, product

Cited by 0

AIDS: A Leslie matrix representation

Jason R. Thomas, Samuel J. Clark, C Jason R. Thomas et al. · 2013

Demographic Research a free, expedited, online journal of peer-reviewed research and commentary in the population sciences published by the

Cited by 0

Multidimensional-matrix representation of tensor

Mukha, V. S. · Репозиторий БГУИР (BSUIR Repository) · 2022

The multidimensional-matrix representation of the arbitrary order tensor is represented which is the generalization of the known matrix representation of the second order tensor. It is showed that the elements of multidimensional matrix of the initial moments of the random vector are the components of the tensor of the respective order.

Cited by 0