• 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.

• Honam Mathematical Journal
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• v.44 no.2
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• pp.195-208
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• 2022

In this article, the matrix representation of commutative elliptic octonions and their properties are described. Firstly, definitions and theorems are given for the commutative elliptic octonion matrices using the elliptic quaternion matrices. Then the adjoint matrix, eigenvalue and eigenvector of the commutative elliptic octonions are investigated. Finally, α = -1 for the Gershgorin Theorem is proved using eigenvalue and eigenvector of the commutative elliptic octonion matrix.

• Journal of information and communication convergence engineering
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• v.15 no.3
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• pp.137-142
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• 2017

A general linearly constrained narrowband adaptive array is examined in the eigenvector space. The optimum weight vector in the eigenvector space is shown to have the same performance as in the standard coordinate system, except that the input signal correlation matrix and look direction steering vector are replaced with the eigenvalue matrix and transformed steering vector. It is observed that the variation in gain factor results in the variation in the distance between the constraint plane and the origin in the translated weight vector space such that the increase in gain factor decreased the distance from the constraint plane to the origin, thus affecting the nulling performance. Simulation results showed that the general linearly constrained adaptive array performed better at an optimal gain factor compared with the conventional linearly constrained adaptive array in a coherent signal environment and the former showed similar performance as the latter in a noncoherent signal environment.

• Journal of the Korean Statistical Society
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• v.24 no.1
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• pp.183-195
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• 1995

For a distribution on the unit sphere, the set of eigenvectors of the second moment matrix is a conventional measure of orientation. Asymptotic confidence cones for eigenvector under the parametric assumptions for the underlying distributions and nonparametric confidence cones for eigenvector based on bootstrapping were proposed. In this paper, to reduce the level error of confidence cones for eigenvector, double bootstrap confidence cones based on prepivoting are considered, and the consistency of this method is discussed. We compare the perfomances of double bootstrap method with the others by Monte Carlo simulations.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2003.04a
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• pp.39-44
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• 2003

It was shown that the robustness of deterministic observers with respect to modeling errors, measurement bias and round-off errors can be represented by a single performance index the condition number of the observer eigenvector matrix. In this paper, a robust observer for multi-output systems is designed using the left eigenstructure assignment, where the observer gain can not be determined uniquely with respect to the desired observer poles. Utilizing the eigenstructuer assignment for the robustness of the observer, the desired eigenvector matrix is selected to achieve the observer eigenvector matrix with the small condition number. The performance of the designed robust observer is evaluated in a spindle-drive simulation example where the load speed to be estimated based on the measured signals.

• Phonetics and Speech Sciences
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• v.1 no.1
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• pp.69-73
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• 2009

This paper proposes an efficient global covariance-based principal component analysis (GCPCA) for speaker identification. Principal component analysis (PCA) is a feature extraction method which reduces the dimension of the feature vectors and the correlation among the feature vectors by projecting the original feature space into a small subspace through a transformation. However, it requires a larger amount of training data when performing PCA to find the eigenvalue and eigenvector matrix using the full covariance matrix by each speaker. The proposed method first calculates the global covariance matrix using training data of all speakers. It then finds the eigenvalue matrix and the corresponding eigenvector matrix from the global covariance matrix. Compared to conventional PCA and Gaussian mixture model (GMM) methods, the proposed method shows better performance while requiring less storage space and complexity in speaker identification.

• Journal of information and communication convergence engineering
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• v.15 no.2
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• pp.73-78
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• 2017

A general linearly constrained broadband adaptive array is examined in the eigenvector space with respect to the optimal weight vector and the adaptive algorithm. The optimal weight vector and the general adaptive algorithm in the eigenvector space are obtained by eigenvector matrix transformation. Their operations are shown to be the same as in the standard coordinate system except for the relevant transformed vectors and matrices. The nulling performance of the general linearly constrained broadband adaptive array depends on the gain factor such that the constraint plane is shifted perpendicularly to the origin by an increase in the gain factor. The general linearly constrained broadband adaptive array is observed to perform better than a conventional linearly constrained adaptive array in a coherent signal environment, while the former performs similarly to the latter in a non-coherent signal environment.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.6
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• pp.1114-1119
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• 2002

In this paper, the well-conditioned observer is designed to be insensitive to the ill-conditioning factors in transient and steady-state observer performance. A condition number based on 12-norm of the eigenvector matrix of the observer matrix has been proposed on a principal index in the observer performance. For the well-conditioned observer design, the non-normality measure and the observability condition of the observer matrix are utilized. The two constraints are specified into observer gain boundary region that guarantees a small condition number and a stable observer. The observer gain selected in this region guarantees a well-conditioned and observable property. In this study, this method is applied to the Luenberger observer and Kalman filters for small order systems. In designing Kalman filters, the ratio of the process noise covariance to the measurement noise covariance is a design parameter and its effect on the condition number is investigated.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2001.10a
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• pp.313-318
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• 2001

In this paper, the well-conditioned observer is designed to be insensitive to the ill-conditioning factors in transient and steady-state observer performance. A condition number based on $L_2-norm$ of the eigenvector matrix of the observer matrix has been proposed on a principal index in the observer performance. For the well-conditioned observer design, the non-normality measure and the observability condition of the observer matrix are utilized. The two constraints are specified into observer gain boundary region that guarantees a small condition number and a stable observer. The observer gain selected in this region guarantees a well-conditioned and observable property. In this study, this method is applied to the Luenberger observer and Kalman filters. In designing Kalman filters for small order systems, the ratio of the process noise covariance to the measurement noise covariance is a design parameter and its effect on the condition number is investigated.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.2
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• pp.340-346
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• 1996

In this paper, we propose a ne weighted backward covariance matrix method to enhance the resolution for direction-of-arrival(DOA) estimation. The proposed method (MEVM:modified eigenvector method) is an enhanced covariance matrix method which is an extended form of the conventional covariance matrix. We analyze the effect of using the weighted forward-baskward covariance matrix on the performance of the eigenvector method(EVM). By comparing the perturbation angle of the noise-subspace, we show that the spectral estimate obtained using the proposed method is less distorted than the spectral estimate obtained using the conventional EVM. The simulation results show that the new method is more accurate and has better resolution than the conventional EVM under the same noise conditions.