The matrix representations of g2. II. Representations in an su(3) basis

1988 ◽  
Vol 29 (4) ◽  
pp. 767-776 ◽  
Author(s):  
R. Le Blanc ◽  
D. J. Rowe
Keyword(s):  
Matrix Representations ◽  
The Matrix

scholarly journals EXTENSION OF THE POINCARÉ GROUP AND NON-ABELIAN TENSOR GAUGE FIELDS

2010 ◽  
Vol 25 (31) ◽  
pp. 5765-5785 ◽  
Author(s):  
GEORGE SAVVIDY
Keyword(s):  
Gauge Group ◽  
Gauge Transformation ◽  
Space Time ◽  
Gauge Fields ◽  
Poincaré Group ◽  
Matrix Representations ◽  
Poincare Group ◽  
Yang Mills ◽  
The Matrix ◽  
Transversal Plane

In the recently proposed generalization of the Yang–Mills theory, the group of gauge transformation gets essentially enlarged. This enlargement involves a mixture of the internal and space–time symmetries. The resulting group is an extension of the Poincaré group with infinitely many generators which carry internal and space–time indices. The matrix representations of the extended Poincaré generators are expressible in terms of Pauli–Lubanski vector in one case and in terms of its invariant derivative in another. In the later case the generators of the gauge group are transversal to the momentum and are projecting the non-Abelian tensor gauge fields into the transversal plane, keeping only their positively definite spacelike components.

scholarly journals Computing mu-values for Representations of Symmetric Groups in Engineering Systems

2018 ◽  
Vol 11 (3) ◽  
pp. 774-792
Author(s):  
Mutti-Ur Rehman ◽  
M. Fazeel Anwar
Keyword(s):  
Control Systems ◽  
Symmetric Groups ◽  
Singular Values ◽  
Linear Control ◽  
Linear Control Systems ◽  
Complex Numbers ◽  
Engineering Systems ◽  
Matrix Representations ◽  
The Matrix

In this article we consider the matrix representations of finite symmetric groups Sn over the filed of complex numbers. These groups and their representations also appear as symmetries of certain linear control systems [5]. We compute the structure singular values (SSV) of the matrices arising from these representations. The obtained results of SSV are compared with well-known MATLAB routine mussv.

scholarly journals Hashing Based Answer Selection

2020 ◽  
Vol 34 (05) ◽  
pp. 9330-9337
Author(s):  
Dong Xu ◽  
Wu-Jun Li
Keyword(s):  
Question Answering ◽  
Matrix Representation ◽  
Matrix Representations ◽  
Binary Matrix ◽  
Large Memory ◽  
The Matrix ◽  
Novel Method ◽  
Online Prediction ◽  
Memory Cost ◽  
Vector Representations

Answer selection is an important subtask of question answering (QA), in which deep models usually achieve better performance than non-deep models. Most deep models adopt question-answer interaction mechanisms, such as attention, to get vector representations for answers. When these interaction based deep models are deployed for online prediction, the representations of all answers need to be recalculated for each question. This procedure is time-consuming for deep models with complex encoders like BERT which usually have better accuracy than simple encoders. One possible solution is to store the matrix representation (encoder output) of each answer in memory to avoid recalculation. But this will bring large memory cost. In this paper, we propose a novel method, called hashing based answer selection (HAS), to tackle this problem. HAS adopts a hashing strategy to learn a binary matrix representation for each answer, which can dramatically reduce the memory cost for storing the matrix representations of answers. Hence, HAS can adopt complex encoders like BERT in the model, but the online prediction of HAS is still fast with a low memory cost. Experimental results on three popular answer selection datasets show that HAS can outperform existing models to achieve state-of-the-art performance.

scholarly journals Construction of generalized rotations and quasi-orthogonal matrices

2019 ◽  
Vol 7 (1) ◽  
pp. 107-113
Author(s):  
Luis Verde-Star
Keyword(s):  
Image Processing ◽  
Hadamard Matrices ◽  
Complex Numbers ◽  
Data Communications ◽  
Matrix Representations ◽  
Orthogonal Matrices ◽  
Orthogonal Designs ◽  
The Matrix ◽  
The One

Abstract We propose some methods for the construction of large quasi-orthogonal matrices and generalized rotations that may be used in applications in data communications and image processing. We use certain combinations of constructions by blocks similar to the one used by Sylvester to build Hadamard matrices. The orthogonal designs related with the matrix representations of the complex numbers, the quaternions, and the octonions are used in our construction procedures.

Matrix representations of right ample semigroups

2015 ◽  
Vol 08 (03) ◽  
pp. 1550042 ◽  
Author(s):  
Junying Guo ◽  
Xiaojiang Guo ◽  
K. P. Shum
Keyword(s):  
Matrix Representation ◽  
Matrix Representations ◽  
Ample Semigroup ◽  
The Matrix

The properties of right ample semigroups have been extensively considered and studied by many authors. In this paper, we concentrate on the matrix representations of right ample semigroups. The (left; right) uniform matrix representation is initially defined. After some properties of left uniform matrix representations of a right ample semigroup are given, we prove that any irreducible left uniform representations of a right ample semigroup can be obtained by using an irreducible left uniform representation of some primitive right ample semigroup. In particular, a construction theorem of prime left uniform representation of right ample semigroups is established.

Building combined MRP-matrices with BuM, an automated web-tool

Zootaxa ◽  
2019 ◽  
Vol 4567 (2) ◽  
pp. 387
Author(s):  
MUHSEN HAMMOUD ◽  
JOÃO PAULO GOIS ◽  
DAUBIAN SANTOS ◽  
STEPHANIE SAMPRONHA ◽  
CHARLES MORPHY D. SANTOS
Keyword(s):  
Phylogenetic Trees ◽  
Web Tool ◽  
Matrix Representations ◽  
Online Tool ◽  
Coding Scheme ◽  
The Matrix ◽  
Tree Methods ◽  
The Individual ◽  
Single Matrix ◽  
Individual Trees

The most common methods for combining different phylogenetic trees with uneven but overlapping taxon sampling are the Matrix Representation with Parsimony (MRP) and consensus tree methods. Although straightforward, some steps of MRP are time-consuming and risky when manually performed, especially the preparation of the matrix representations from the original topologies, and the creation of the single matrix containing all the information of the individual trees. Here we present Building MRP-Matrices (BuM), a free online tool for generating a combined matrix, following Baum and Ragan coding scheme, from files containing phylogenetic trees in parenthetical format. 

L-2 DEGREE REDUCTION OF TRIANGULAR BÉZIER SURFACES WITH COMMON TANGENT PLANES AT VERTICES

2005 ◽  
Vol 15 (05) ◽  
pp. 477-490 ◽  
Author(s):  
ABEDALLAH RABABAH
Keyword(s):  
Closed Form ◽  
Error Term ◽  
Least Squares Method ◽  
Computational Cost ◽  
Degree Reduction ◽  
Common Tangent ◽  
Matrix Representations ◽  
Bézier Surfaces ◽  
The Matrix ◽  
Bezier Surfaces

In this paper, we present a method of degree reduction for triangular Bézier surfaces. The approximate and the original triangular Bézier surfaces have common tangent planes at the vertices. We use the least squares method with the L 2 and l2 norms to get a closed form for the reduction of the degree and show that both solutions are the same. This scheme uses the matrix representations of the degree raising and the Bézier control vertices. The computational cost of the method is evaluated. The error term is derived and a numerical example is given.

scholarly journals Minimal linear representations of the low-dimensional nilpotent Lie algebras

2008 ◽  
Vol 102 (1) ◽  
pp. 17 ◽  
Author(s):  
J. C. Benjumea ◽  
J. Núnez ◽  
A. F. Tenorio
Keyword(s):  
Lie Algebras ◽  
Nilpotent Lie Algebra ◽  
Matrix Representations ◽  
Triangular Matrices ◽  
Nilpotent Lie Algebras ◽  
Linear Representations ◽  
Minimal Dimension ◽  
The Matrix ◽  
Low Dimensional

The main goal of this paper is to compute a minimal matrix representation for each non-isomorphic nilpotent Lie algebra of dimension less than $6$. Indeed, for each of these algebras, we search the natural number $n\in\mathsf{N}\setminus\{1\}$ such that the linear algebra $\mathfrak{g}_n$, formed by all the $n \times n$ complex strictly upper-triangular matrices, contains a representation of this algebra. Besides, we show an algorithmic procedure which computes such a minimal representation by using the Lie algebras $\mathfrak{g}_n$. In this way, a classification of such algebras according to the dimension of their minimal matrix representations is obtained. In this way, we improve some results by Burde related to the value of the minimal dimension of the matrix representations for nilpotent Lie algebras.

scholarly journals Pauli–Fibonacci quaternions

2021 ◽  
Vol 27 (3) ◽  
pp. 184-193
Author(s):  
Fügen Torunbalcı Aydın ◽  
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Matrix Representations ◽  
The Matrix ◽  
Binet’S Formula

The aim of this work is to consider the Pauli–Fibonacci quaternions and to present some properties involving this sequence, including the Binet’s formula and generating functions. Furthermore, the Honsberger identity, the generating function, d’Ocagne’s identity, Cassini’s identity, Catalan’s identity for these quaternions are given. The matrix representations for Pauli–Fibonacci quaternions are introduced.

scholarly journals Eigenvalues of matrices related to the octonions

4open ◽  
2019 ◽  
Vol 2 ◽  
pp. 16
Author(s):  
Rogério Serôdio ◽  
Patricia Beites ◽  
José Vitória
Keyword(s):  
Matrix Representation ◽  
Real Matrix ◽  
Matrix Representations ◽  
Estimation Algorithms ◽  
The Matrix

A pseudo real matrix representation of an octonion, which is based on two real matrix representations of a quaternion, is considered. We study how some operations defined on the octonions change the set of eigenvalues of the matrix obtained if these operations are performed after or before the matrix representation. The established results could be of particular interest to researchers working on estimation algorithms involving such operations.

Sign in / Sign up

Export Citation Format

Share Document