• 제어로봇시스템학회논문지
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• 제14권3호
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• pp.226-231
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• 2008

In this paper, we propose novel eigenstructure assignment method in full-state feedback for linear time-invariant MIMO system such that directions of some left eigenvectors are exactly assigned to the desired directions. It is required to consider the direction of left eigenvector in designing eigenstructure of closed-loop system, because the direction of left eigenvector has influence over excitation by associated input variables in time-domain response. Exact direction of a left eigenvector can be achieved by assigning proper right eigenvector set satisfying the conditions of the presented theorem based on Moore's theorem and the orthogonality of left and right eigenvector. The right eigenvector should reside in the subspace given by the desired eigenvalue, which restrict a number of designable left eigenvector. For the two cases in which desired eigenvalues are all real and contain complex number, design freedom of designable left eigenvector are given.

• 한국수학교육학회지시리즈A:수학교육
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• 제51권1호
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• pp.77-88
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• 2012

This qualitative research provides a situation model, which is designed for promoting learning of eigenvalue and eigenvector. This study also demonstrates the usefulness of the model through a small groups discussion. Particularly, participants of the discussion were asked to decide the numbers of milk cows in order to make constant amounts of cheese production. Through such discussions, subjects understood the notion of eigenvalue and eigenvector. This study has following implications. First of all, the present research finds significance of situation model. A situation model is useful to promote learning of mathematical notions. Subjects learn the notion of eigenvalue and eigenvector through the situation model without difficulty. In addition, this research demonstrates potentials of small groups discussion. Learners participate in discussion more actively under small group debates. Such active interaction is necessary for situation model. Moreover, this study emphasizes the role of teachers by showing that patience and encouragement of teachers promote students' feeling of achievement. The role of teachers are also important in conveying a meaning of eigenvalue and eigenvector. Therefore, this study concludes that experience of learning the notion of eigenvalue and eigenvector thorough situation model is important for teachers in future.

• Journal of the Korean Statistical Society
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• 제24권1호
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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.

• Journal of information and communication convergence engineering
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• 제15권2호
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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.

• 대한기계학회논문집A
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• 제33권1호
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• pp.27-33
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• 2009

Human postural responses appeared to have stereotyped modality, such as ankle mode, knee mode and hip mode in response to various perturbations. We examined whether human postural control gain of full-state feedback could be decoupled along with the eigenvector. To verify the model, postural responses subjected to fast backward perturbation were used. Upright posture was modeled as 3-segment inverted pendulum incorporated with feedback control, and joint torques were calculated using inverse dynamics. Postural modalities such as ankle, knee and hip mode were obtained from eigenvectors of biomechanical model. As oppose to the full-state feedback control, independent eigenvector control assumes that modal control input is determined by the linear combination of corresponding modality. We used optimization method to obtain and compare the feedback gains for both independent eigenvector control and full-state feedback control. As a result, we found that simulation result of eigenvector feedback was not competitive in comparison with that of full-state feedback control. This implies that the CNS would make use of full-state body information to generate compensative joint torques.

• 한국강구조학회 논문집
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• 제8권3호통권28호
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• pp.21-34
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• 1996

A numerical method is presented for computation of eigenvector derivatives used an iterative procedure with guaranteed convergence. An approach for treating the singularity in calculating the eigenvector derivatives is presented, in which a shift in each eigenvalue is introduced to avoid the singularity. If the shift is selected properly, the proposed method can give very satisfactory results after only one iteration. A criterion for choosing an adequate shift, dependent on computer hardware is suggested ; it is directly dependent on the eigenvalue magnitudes and the number of bits per numeral of the computer. Another merit of this method is that eigenvector derivatives with repeated eigenvalues can be easily obtained if the new eigenvectors are calculated. These new eigenvectors lie "adjacent" to the m (number of repeated eigenvalues) distinct eigenvectors, which appear when the design parameter varies. As an example to demonstrate the efficiency of the proposed method in the case of distinct eigenvalues, a cantilever plate is considered. The results are compared with those of Nelson's method which can find the exact eigenvector derivatives. For the case of repeated eigenvalues, a cantilever beam is considered. The results are compared with those of Dailey's method which also can find the exact eigenvector derivatives. The design parameter of the cantilever plate is its thickness, and that of the cantilever beam its height.

• Journal of applied mathematics & informatics
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• 제33권3_4호
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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.

• 한국음향학회지
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• 제23권4호
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• pp.282-287
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• 2004

본 논문에서는 참조 신호에 대한 근거리 신호 모델링 기반의 어레이 형상 추정 기법인 근거리 고유벡터 기법을 제안한다. 수중 음원의 방향을 탐지하기 위한 기법들은 일반적으로 참조 신호를 평면파로 가정하고 있다. 그러나 참조 신호가 근거리에 존재하는 경우 평면파 가정으로는 어레이 형상 추정이 불가능하다. 본 논문에서는 참조 신호가 근거리에 존재하는 경우를 위하여 근거리 신호를 모델링하고 이를 기반으로 근거리 고유벡터 기법을 제안하였다. 또한 모의실험을 통해 제안된 기법이 참조 신호의 거리에 관계없이 우수한 형상 추정 성능을 보임을 확인하였다.

• Journal of information and communication convergence engineering
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• 제15권3호
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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.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 춘계학술대회논문집A
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• pp.115-120
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• 2000

This paper examines that it is possible to apply RWCIM for determining eigenvector coefficients associated with eigenvalues for V-notched cracks in anisotropic dissimilar materials using the complex stress function. To verify the RWCIM algorithm, two tests will be shown. First it is performed to ascertain whether predicted coefficients associated with eigenvectors is obtained exactly. Second, it makes an examination of the state of stress for FEM and RWCIM according to a number of eigenvectors at a location far away from the V-notched crack tip.