Some Results of the Matrix Theory

2013 ◽  
pp. 25-52
Author(s):  
Michael I. Gil’
Keyword(s):  
Matrix Theory ◽  
The Matrix

scholarly journals Partial Component Consensus of Discrete-Time Multiagent Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-5
Author(s):  
Wenjun Hu ◽  
Gang Zhang ◽  
Zhongjun Ma ◽  
Binbin Wu
Keyword(s):  
Multiagent Systems ◽  
Discrete Time ◽  
Matrix Theory ◽  
Pinning Control ◽  
Directed Network ◽  
Strong Function ◽  
Partial Stability ◽  
Partial Component ◽  
The Matrix ◽  
Error System

The multiagent system has the advantages of simple structure, strong function, and cost saving, which has received wide attention from different fields. Consensus is the most basic problem in multiagent systems. In this paper, firstly, the problem of partial component consensus in the first-order linear discrete-time multiagent systems with the directed network topology is discussed. Via designing an appropriate pinning control protocol, the corresponding error system is analyzed by using the matrix theory and the partial stability theory. Secondly, a sufficient condition is given to realize partial component consensus in multiagent systems. Finally, the numerical simulations are given to illustrate the theoretical results.

scholarly journals MATRIX THEORY, HILBERT SCHEME AND INTEGRABLE SYSTEM

1998 ◽  
Vol 13 (34) ◽  
pp. 2731-2742 ◽  
Author(s):  
YUTAKA MATSUO
Keyword(s):  
Hilbert Scheme ◽  
Matrix Theory ◽  
Fock Space ◽  
Homology Class ◽  
Orthogonal Basis ◽  
Inner Product ◽  
Virasoro Symmetry ◽  
Hilbert Scheme Of Points ◽  
The Matrix ◽  
Boson Fock Space

We give a reinterpretation of the matrix theory discussed by Moore, Nekrasov and Shatashivili (MNS) in terms of the second quantized operators which describes the homology class of the Hilbert scheme of points on surfaces. It naturally relates the contribution from each pole to the inner product of orthogonal basis of free boson Fock space. These bases can be related to the eigenfunctions of Calogero–Sutherland (CS) equation and the deformation parameter of MNS is identified with coupling of CS system. We discuss the structure of Virasoro symmetry in this model.

An Improved Method for Calculating Free Vibrations in Systems of Several Degrees of Freedom

1938 ◽  
Vol 5 (2) ◽  
pp. A61-A66
Author(s):  
Winston M. Dudley
Keyword(s):  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Matrix Theory ◽  
Free Vibrations ◽  
Initial Disturbance ◽  
Improved Method ◽  
Matrix Methods ◽  
Computing Machine ◽  
The Matrix ◽  
Time Required

Abstract In 1934 two English investigators (1) published a method for calculating the various modes and frequencies of vibration of a system having several degrees of freedom. Their method, which is based on matrices, greatly shortens the time spent in obtaining numerical solutions in many important problems, notably those with immovable foundations. In this paper is presented a new theorem which (a) makes possible a further reduction of nearly one half in the time required, so that solutions up to 20 deg or more of freedom are now practical and (b) makes it then possible to determine the motion of the system after any initial disturbance in a few minutes, instead of several hours as required by older methods. It is useful in the latter respect whether the modes have been determined by matrix methods, or not. Although the paper gives simpler proofs than any previously published, knowledge of the matrix theory is not required in using the method. Problems are analyzed by a tabular process, in which an ordinary computing machine helps greatly. Comments based on computing experience are given. A simple numerical example has been given elsewhere (1).

Multiconsensus of first-order multiagent systems with directed topologies

2020 ◽  
Vol 34 (23) ◽  
pp. 2050240
Author(s):  
Xiao-Wen Zhao ◽  
Guangsong Han ◽  
Qiang Lai ◽  
Dandan Yue
Keyword(s):  
Multiagent Systems ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Consensus Problem ◽  
Multiple Agents ◽  
First Order ◽  
The Matrix ◽  
Directed Topologies ◽  
Necessary And Sufficient ◽  
Theoretical Results

The multiconsensus problem of first-order multiagent systems with directed topologies is studied. A novel consensus problem is introduced in multiagent systems — multiconsensus. The states of multiple agents in each subnetwork asymptotically converge to an individual consistent value in the presence of information exchanges among subnetworks. Linear multiconsensus protocols are proposed to solve the multiconsensus problem, and the matrix corresponding to the protocol is designed. Necessary and sufficient conditions are derived based on matrix theory, under which the stationary multiconsensus and dynamic multiconsensus can be reached. Simulations are provided to demonstrate the effectiveness of the theoretical results.

scholarly journals On the limiting spectral density of random matrices filled with stochastic processes

2019 ◽  
Vol 27 (2) ◽  
pp. 89-105 ◽  
Author(s):  
Matthias Löwe ◽  
Kristina Schubert
Keyword(s):  
Stochastic Process ◽  
Spectral Density ◽  
Random Matrices ◽  
Markov Processes ◽  
Random Matrix ◽  
Matrix Theory ◽  
Gibbs Measures ◽  
State Spaces ◽  
The Matrix ◽  
Finite State

Abstract We discuss the limiting spectral density of real symmetric random matrices. In contrast to standard random matrix theory, the upper diagonal entries are not assumed to be independent, but we will fill them with the entries of a stochastic process. Under assumptions on this process which are satisfied, e.g., by stationary Markov chains on finite sets, by stationary Gibbs measures on finite state spaces, or by Gaussian Markov processes, we show that the limiting spectral distribution depends on the way the matrix is filled with the stochastic process. If the filling is in a certain way compatible with the symmetry condition on the matrix, the limiting law of the empirical eigenvalue distribution is the well-known semi-circle law. For other fillings we show that the semi-circle law cannot be the limiting spectral density.

scholarly journals MVDR Algorithm Based on Estimated Diagonal Loading for Beamforming

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Yuteng Xiao ◽  
Jihang Yin ◽  
Honggang Qi ◽  
Hongsheng Yin ◽  
Gang Hua
Keyword(s):  
Signal Processing ◽  
Covariance Matrix ◽  
Optimization Model ◽  
Matrix Theory ◽  
Minimum Variance ◽  
Signal Model ◽  
Diagonal Loading ◽  
Minimum Variance Distortionless Response ◽  
The Matrix ◽  
Beamforming Algorithm

Beamforming algorithm is widely used in many signal processing fields. At present, the typical beamforming algorithm is MVDR (Minimum Variance Distortionless Response). However, the performance of MVDR algorithm relies on the accurate covariance matrix. The MVDR algorithm declines dramatically with the inaccurate covariance matrix. To solve the problem, studying the beamforming array signal model and beamforming MVDR algorithm, we improve MVDR algorithm based on estimated diagonal loading for beamforming. MVDR optimization model based on diagonal loading compensation is established and the interval of the diagonal loading compensation value is deduced on the basis of the matrix theory. The optimal diagonal loading value in the interval is also determined through the experimental method. The experimental results show that the algorithm compared with existing algorithms is practical and effective.

MODELING THE DYNAMIC INTERACTION PROCESSES USING OF FUZZY TIMED PETRI NETS OF TYPE VF

2019 ◽  
pp. 19-26
Author(s):  
V. A. Mustafayev ◽  
M. N. Salmanova
Keyword(s):  
Petri Nets ◽  
Matrix Theory ◽  
Production Model ◽  
Timed Petri Nets ◽  
Complex Objects ◽  
Structure Representation ◽  
Effective Form ◽  
The Matrix ◽  
Composition Laws ◽  
Analysis Models

The dynamic interacting processes modeling is examined in the article, which shows the complex objects operation in the condition of uncertainty. A formalism intended for the development and analysis models of complex parallel and distributed systems is proposed. It is based on the mathematical apparatus of the fuzzy timed Petri nets (FTPN) of type Vf, representing generalized FTPN of type Vf , combining deterministic and non-deterministic character. The algorithm for the functioning FTPN of type Vf is developed. The proposed algorithm provides a solution to the problem of the triggering solvability of transitions occurring in conflict states, the imposition of a fuzzy structure on the network marking with fuzzy composition laws that determine the values the degrees of belonging the input and output transition positions. The model of parallel functioning processing devices is presented in the FTPN form of type Vf. An approach is proposed for modeling dynamic interacting processes based on the matrix theory of Petri nets, that provides an effective form of structure representation, model state dynamics, the space of achievable states, and triggering transitions sequence in the form of vectors and matrices set. On the example of the production model of mechanical processing, it is shown that the accepted triggering transitions rules fully show the functioning FTPN process of type Vf. As a result of the simulation, the reachability tree is obtained as a sequence of matrices.

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