scholarly journals Pembentukan Grup Matriks Singular 2×2

2021 ◽  
Vol 1 (3) ◽  
pp. 403-411
Author(s):  
Ery Nurjayanto ◽  
Amrullah Amrullah ◽  
Arjudin Arjudin ◽  
Sudi Prayitno
Keyword(s):  
Abelian Group ◽  
Higher Order ◽  
Nonsingular Matrix ◽  
Matrix Group ◽  
Exploratory Research ◽  
Singular Matrix ◽  
Generator Matrix ◽  
Matrix Groups ◽  
The Matrix ◽  
Pseudo Inverse

The study aims to determine the set of the singular matrix 2×2 that forms the group and describes its properties. The type of research was used exploratory research. Using diagonalization of the singular matrix  S, whereas a generator matrix, pseudo-identity, and pseudo-inverse methods, we obtained a group singular matrix 2×2  with standard multiplication operations on the matrix, with conditions namely:    (1) closed, (2) associative, (3) there was an element of identity, (4) inverse, there was (A)-1 so A x (A)-1 = (A)-1 x A = Is. The group was the abelian group (commutative group). In addition, in the group, Gs satisfied that if Ɐ A, X, Y element Gs was such that A x X = A x Y then X = Y and X x A = Y x A then X = Y. This show that the group can be applied the cancellation properties like the case in nonsingular matrix group. This research provides further research opportunities on the formation of singular matrix groups 3×3 or higher order.

scholarly journals A Numerical Method for Computing the Roots of Non-Singular Complex-Valued Matrices

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 966
Author(s):  
Diego Caratelli ◽  
Paolo Emilio Ricci
Keyword(s):  
Numerical Method ◽  
Worked Examples ◽  
Higher Order ◽  
Singular Matrix ◽  
The Matrix ◽  
General Complex ◽  
Complex Valued

A method for the computation of the n th roots of a general complex-valued r × r non-singular matrix ? is presented. The proposed procedure is based on the Dunford–Taylor integral (also ascribed to Riesz–Fantappiè) and relies, only, on the knowledge of the invariants of the matrix, so circumventing the computation of the relevant eigenvalues. Several worked examples are illustrated to validate the developed algorithm in the case of higher order matrices.

2D Structural Acoustic Analysis Using the FEM/FMBEM with Different Coupled Element Types

2017 ◽  
Vol 42 (1) ◽  
pp. 37-48 ◽  
Author(s):  
Leilei Chen ◽  
Wenchang Zhao ◽  
Cheng Liu ◽  
Haibo Chen
Keyword(s):  
Acoustic Analysis ◽  
Interaction Analysis ◽  
Fast Multipole Method ◽  
Boundary Elements ◽  
Higher Order ◽  
Boundary Integral ◽  
The Matrix ◽  
Coupling Approach ◽  
Element Type ◽  
Relative Errors

Abstract A FEM-BEM coupling approach is used for acoustic fluid-structure interaction analysis. The FEM is used to model the structure and the BEM is used to model the exterior acoustic domain. The aim of this work is to improve the computational efficiency and accuracy of the conventional FEM-BEM coupling approach. The fast multipole method (FMM) is applied to accelerating the matrix-vector products in BEM. The Burton-Miller formulation is used to overcome the fictitious eigen-frequency problem when using a single Helmholtz boundary integral equation for exterior acoustic problems. The continuous higher order boundary elements and discontinuous higher order boundary elements for 2D problem are developed in this work to achieve higher accuracy in the coupling analysis. The performance for coupled element types is compared via a simple example with analytical solution, and the optimal element type is obtained. Numerical examples are presented to show the relative errors of different coupled element types.

scholarly journals Higher-order Darboux transformations for two-dimensional Dirac systems with diagonal matrix potential

2021 ◽  
Vol 2090 (1) ◽  
pp. 012038
Author(s):  
A Schulze-Halberg
Keyword(s):  
Dirac Equation ◽  
Explicit Form ◽  
Higher Order ◽  
Diagonal Matrix ◽  
Two Dimensional ◽  
Darboux Transformations ◽  
Dirac Systems ◽  
Matrix Potential ◽  
De Vries ◽  
The Matrix

Abstract We construct the explicit form of higher-order Darboux transformations for the two-dimensional Dirac equation with diagonal matrix potential. The matrix potential entries can depend arbitrarily on the two variables. Our construction is based on results for coupled Korteweg-de Vries equations [27].

Matrix Group Actions Transforming Patterns

2006 ◽  
Author(s):  
Ulf Grenander ◽  
Michael I. Miller
Keyword(s):  
Coordinate System ◽  
Spatial Patterns ◽  
Group Actions ◽  
Temporal Patterns ◽  
Matrix Group ◽  
Matrix Groups ◽  
Pattern Theory ◽  
Complex Patterns

Thus far Pattern theory has been combinatore constructing complex patterns by connecting simpler ones via graphs. Patterns typically occurring in nature may be extremely complex and exhibit invariances. For example, spatial patterns may live in a space where the choice of coordinate system is irrelevant; temporal patterns may exist independently of where time is counted from, and so on. For this matrix groups as transformations are introduced, these transformations often forming groups which act on the generators.

scholarly journals Generalized Inverses Estimations by Means of Iterative Methods with Memory

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 2
Author(s):  
Santiago Artidiello ◽  
Alicia Cordero ◽  
Juan R. Torregrosa ◽  
María P. Vassileva
Keyword(s):  
Iterative Methods ◽  
Generalized Inverses ◽  
Drazin Inverse ◽  
Nonsingular Matrix ◽  
Type Method ◽  
The Matrix ◽  
Nonlinear Matrix ◽  
First Time ◽  
With Memory ◽  
Theoretical Results

A secant-type method is designed for approximating the inverse and some generalized inverses of a complex matrix A. For a nonsingular matrix, the proposed method gives us an approximation of the inverse and, when the matrix is singular, an approximation of the Moore–Penrose inverse and Drazin inverse are obtained. The convergence and the order of convergence is presented in each case. Some numerical tests allowed us to confirm the theoretical results and to compare the performance of our method with other known ones. With these results, the iterative methods with memory appear for the first time for estimating the solution of a nonlinear matrix equations.

FERMI SYSTEMS, HUBBARD MODEL AND A SYMBOLICC++ IMPLEMENTATION

2001 ◽  
Vol 12 (02) ◽  
pp. 235-245 ◽  
Author(s):  
YORICK HARDY ◽  
WILLI-HANS STEEB
Keyword(s):  
Hubbard Model ◽  
Computer Algebra ◽  
Matrix Representation ◽  
Higher Order ◽  
Fermi Systems ◽  
The Matrix ◽  
Constants Of Motion

We show how the anticommutation relations for Fermi operators can be implemented with computer algebra using SymbolicC++. We describe applications to the Hubbard model. An important identity for Fermi operators is proved. Then, we test for higher order constants of motion for the Hubbard model. Finally, the matrix representation for the four point Hubbard model is calculated.

scholarly journals A recognition algorithm for non-generic classical groups over finite fields

1999 ◽  
Vol 67 (2) ◽  
pp. 223-253 ◽  
Author(s):  
Azice C. Niemeyer ◽  
Cheryl E. Praeger
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Special Linear Group ◽  
Theoretical Background ◽  
Recognition Algorithm ◽  
Large Field ◽  
Matrix Group ◽  
Classical Groups ◽  
Original Algorithm ◽  
The Matrix

AbstractIn a previous paper the authors described an algorithm to determine whether a group of matrices over a finite field, generated by a given set of matrices, contains one of the classical groups or the special linear group. The algorithm was designed to work for all sufficiently large field sizes and dimensions of the matrix group. However, it did not apply to certain small cases. Here we present an algorithm to handle the remaining cases. The theoretical background of the algorithm presented in this paper is a substantial extension of that needed for the original algorithm.

scholarly journals Synthesis on the Acceleration Energies in the Advanced Mechanics of the Multibody Systems

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1077 ◽  
Author(s):  
Negrean ◽  
Crișan
Keyword(s):  
Multibody Systems ◽  
Driving Forces ◽  
Higher Order ◽  
Analytical Mechanics ◽  
Polynomial Functions ◽  
Control Functions ◽  
Generalized Variables ◽  
The Matrix ◽  
Matrix Exponentials ◽  
Fifth Order

The present paper’s objective is to highlight some new developments of the main author in the field of advanced dynamics of systems and higher order dynamic equations. These equations have been developed on the basis of the matrix exponentials which prove to have undeniable advantages in the matrix study of any complex mechanical system. The present paper proposes some new approaches, based on differential principles from analytical mechanics, by using some important dynamics notions, regarding the acceleration energies of the first, second and third order. This study extended the equations of the higher order, which provide the possibility of applying the initial motion conditions in the positions, velocities and accelerations of the first and second order. In order to determine the time variation laws for the generalized variables, the driving forces and acceleration energies of the higher order are applied by the time polynomial functions of the fifth order. According to inverse kinematics also named control kinematics of the robots, the applications of polynomial functions lead to the kinematic control functions of mechanical motions, especially the transitory motions. They influence the dynamic behavior of multibody systems, in which robot structures are included.

scholarly journals Solving higher order Fuchs type differential systems avoiding the increase of the problem dimension

1994 ◽  
Vol 17 (1) ◽  
pp. 91-102
Author(s):  
E. Navarro ◽  
L. Jódar ◽  
R. Company
Keyword(s):  
Homogeneous Problem ◽  
Higher Order ◽  
Closed Form Expression ◽  
Power Series Solution ◽  
Matrix Equations ◽  
Form Expression ◽  
Initial Value ◽  
Generalized Power Series ◽  
The Matrix ◽  
Problem Dimension

In this paper, we develop a Frobenius matrix method for solving higher order systems of differential equations of the Fuchs type. Generalized power series solution of the problem are constructed without increasing the problem dimension. Solving appropriate algebraic matrix equations a closed form expression for the matrix coefficient of the series are found. By means of the concept of ak-fundamental set of solutions of the homogeneous problem an explicit solution of initial value problems are given.

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