• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.21 no.2
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• pp.103-109
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• 2021

About the orthogonal Hadamard matrix announced by Hadamard in France in 1893, Professor Moon Ho Lee newly defined it as Center Weight Hadamard in 1989 and announced it, and discovered the Jacket matrix in 1998. The Jacket matrix is a generalization of the Hadamard matrix. In this paper, we propose a method of obtaining the Symmetric Jacket matrix, analyzing important properties and patterns, and obtaining the Jacket matrix's determinant and Eigenvalue, and proved it using Eigen decomposition. These calculations are useful for signal processing and orthogonal code design. To analyze the matrix system, compare it with DFT, DCT, Hadamard, and Jacket matrix. In the symmetric matrix of Galois Field, the element-wise inverse relationship of the Jacket matrix was mathematically proved and the orthogonal property AB=I relationship was derived.

• Journal of Multimedia Information System
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• v.4 no.4
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• pp.219-224
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• 2017

This paper is to introduce an application of face recognition algorithm in parallel. We have experiments of 25 images with different motions and simulated the image recognitions; grouping of the image vectors, image normalization, calculating average image vectors, etc. We also discuss an analysis of the related eigen-image vectors and a parallel algorithm. To develop the parallel algorithm, we propose a new type of initial matrices for eigenvalue problem. If A is a symmetric matrix, initial matrices for eigen value problem are investigated: the "optimal" one, which minimize ${\parallel}C-A{\parallel}_F$ and the "super optimal", which minimize ${\parallel}I-C^{-1}A{\parallel}_F$. In this paper, we present a general new approach to the design of an initial matrices to solving eigenvalue problem based on the new optimal investigating C with preserving the characteristic of the given matrix A. Fast all resulting can be inverted via fast transform algorithms with O(N log N) operations.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.275-285
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• 2013

In this paper a nonlinear matrix equation is considered which has the form $$P(X)=A_0X^m+A_1X^{m-1}+{\cdots}+A_{m-1}X+A_m=0$$ where X is an $n{\times}n$ unknown real matrix and $A_m$, $A_{m-1}$, ${\cdots}$, $A_0$ are $n{\times}n$ matrices with real elements. Newtons method is applied to find the skew-symmetric solvent of the matrix polynomial P(X). We also suggest an algorithm which converges the skew-symmetric solvent even if the Fr$\acute{e}$echet derivative of P(X) is singular.

• KIEE International Transactions on Power Engineering
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• v.5A no.4
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• pp.344-349
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• 2005

In conventional small signal stability analysis, the system is assumed to be invariant and the state space equations are used to calculate the eigenvalues of the state matrix. However, when a system contains switching elements such as FACTS equipments, it becomes a non-continuous system. In this case, a mathematically rigorous approach to system small signal stability analysis is performed by means of eigenvalue analysis of the system's periodic transition matrix based on the discrete system analysis method. In this paper, the RCF (Resistive Companion Form) method is used to analyze the small signal stability of a non-continuous system including switching elements. Applying the RCF method to the differential and integral equations of the power system, generator, controllers and FACTS equipments including switching devices should be modeled in the form of state transition equations. From this state transition matrix, eigenvalues that are mapped into unit circles can be computed precisely.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.247-260
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• 2015

The special form of Schur complement is extended to have a Schur's formula to obtains the explicit formula of determinant, inverse, and eigenvector formula of the doubly Leslie matrix which is the generalized forms of the Leslie matrix. It is also a generalized form of the doubly companion matrix, and the companion matrix, respectively. The doubly Leslie matrix is a nonderogatory matrix.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.5-16
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• 1999

We introduce a new projector for accelerating convergence of a symmetric eigenvalue problem Ax = x, and devise a power/Lanczos hybrid algorithm. Acceleration can be achieved by removing the hard-to-annihilate nonsolution eigencomponents corresponding to the widespread eigenvalues with modulus close to 1, by estimating them accurately using the Lanczos method. However, the additional Lanczos results can be obtained without expensive matrix-vector multiplications but a very small amount of extra work, by utilizing simple power-Lanczos interconversion algorithms suggested. Numerical experiments are given at the end.

• Proceedings of the KIEE Conference
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• 1993.07a
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• pp.54-56
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• 1993

A systematic procedure for determining the elements of system state matrix is suggested. The interrelation of submatrices of the system matrix is investigated. Each element or each block can be represented in algebraic form. These results can be applied in the eigenvalue sensitivity analysis with respect to the changes in controller parameters.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.33A no.11
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• pp.120-127
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• 1996

In the WKB analysis, we propose the new forms of the trial eigenfunctions which not only converge at the turning points but also approximate to the conventional WKB solutions away from the turning points. The eigenvalue equation of multiple waveguides with graded index profile are derived by using the proposed WKB analysis and the transfer matrix method. The drived equation sare represented in the recursive form. The results of the eigenvalue equation sare comapred with those of the FDM, one of the well-known computational methods, for a three-waveguide coupler.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.7
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• pp.794-799
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• 1999

This study deals with robustness bounds estimation for uncertain linear systems with structured perturbations where the eigenvalues of the perturbed systems are guaranteed to stay in a prescribed region. Based upon the Lyapunov approach, new theorems to estimate allowable perturbation parameter bounds are derived. The theorems are referred to as the zero-order or first-order asymmetric robustness measure depending on the order of the P matrix in the sense of Taylor series expansion of perturbed Lyapunov equation. It is proven that Gao's theorem for the estimation of stability robustness bounds is a special case of proposed zero-order asymmetric robustness measure for eigenvalue assignment. Robustness bounds of perturbed parameters measured by the proposed techniques are asymmetric around the origin and less conservative than those of conventional methods. Numerical examples are given to illustrate proposed methods.

• Wind and Structures
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• v.10 no.1
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• pp.61-82
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• 2007

This paper presents a novel finite element (FE) model for analyzing coupled flutter of long-span bridges using the commercial FE package ANSYS. This model utilizes a specific user-defined element Matrix27 in ANSYS to model the aeroelastic forces acting on the bridge, wherein the stiffness and damping matrices are expressed in terms of the reduced wind velocity and flutter derivatives. Making use of this FE model, damped complex eigenvalue analysis is carried out to determine the complex eigenvalues, of which the real part is the logarithm decay rate and the imaginary part is the damped vibration frequency. The condition for onset of flutter instability becomes that, at a certain wind velocity, the structural system incorporating fictitious Matrix27 elements has a complex eigenvalue with zero or near-zero real part, with the imaginary part of this eigenvalue being the flutter frequency. Case studies are provided to validate the developed procedure as well as to demonstrate the flutter analysis of cable-supported bridges using ANSYS. The proposed method enables the bridge designers and engineering practitioners to analyze flutter instability by using the commercial FE package ANSYS.