• Title, Summary, Keyword: Eigenvector

### Direction Assignment of Left Eigenvector in Linear MIMO System (선형 다변수 입출력 시스템에서 좌 고유벡터의 방향 지정)

• Kim, Sung-Hyun;Yang, Hyun-Seok
• Journal of Institute of Control, Robotics and Systems
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• v.14 no.3
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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.

### Students' conceptual development of eigenvalue and eigenvector based on the situation model (상황모델에 기반한 학생들의 고유치와 고유벡터 개념발달)

• Shin, Kyung-Hee
• The Mathematical Education
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• v.51 no.1
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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.

### Double Bootstrap Confidence Cones for Sphericla Data based on Prepivoting

• Shin, Yang-Kyu
• 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.

• Chang, Byong Kun
• 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.

### An Iterative Method for Natural Frequency and Mode Shape Sensitivities (고유진동수와 모우드의 민감도를 구하기 위한 반복법)

• JUNG, GH;JUNG, HJ;OH, JW;LEE, IW
• Journal of Korean Society of Steel Construction
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• v.8 no.3
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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.

### Human Postural Response to Linear Perturbation (선형외란에 대응하는 인체의 자세응답 해석)

• Kim, Se-Young;Park, Su-Kyung
• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.1
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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.

### EXPLICIT MINIMUM POLYNOMIAL, EIGENVECTOR AND INVERSE FORMULA OF DOUBLY LESLIE MATRIX

• WANICHARPICHAT, WIWAT
• 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.

### An Analysis of Eigenvector Coefficient for V-notched Cracks in Pseudo-isotropic and Anisotropic Dissimilar Materials (유사등방성과 이방성 이종재 V-노치 균열의 고유벡터계수 해석)

• Kim, Jin-Gwang;Jo, Sang-Bong
• Journal of the Korean Society for Precision Engineering
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• v.18 no.12
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• pp.88-94
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• 2001
• The V-notched crack problem in dissimilar materials can be formulated as an eigenvalue problem. The RWCIM(Reciprocal Work Contour Integral Method) is applied to the determination of the eigenvector coefficients associated with eigenvalues for V-notched cracks in pseudo-isotropic and anisotropic dissimilar materials. The RWCIM algorithm is programed by the commercial numerical program, MATHEMATICA. The numerical results obtained are shown that the RWCIM is a useful method for determining the eigenvector coefficients of V-notched cracks in pseudo-isotropic and anisotropic dissimilar materials.

### Application of the Reciprocal Work Contour Integral Method to the Analysis of Eigenvector Cofficients for V-notched Cracks in Anistropic Dissimilar Materials (이방성 이종재 V-노치 균열의 고유벡터계수 해석에 대한 상반일 경로 적분법의 적용)

• Jo, Sang-Bong;No, Hong-Rae
• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.9
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• pp.1368-1375
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• 2001
• 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 are obtained exactly. Second, it makes an examination of the state of stresses for FEM and RWCIM according to a number of eigenvectors at a location far away from the v-notched crack tip.

### A study on the eigenvector analyses for V-notched cracks in Anisotropic Dissimilar Materials by the Reciprocal Work Contour Integral Method (상반일 등고선 적분법(RWCIM)을 이용한 이방성 이종재료 내의 V-노치 균열에 대한 고유벡터 해석)

• Roh, Hong-Rae;Kim, Jin-Kwang;Cho, Sang-Bong
• Proceedings of the KSME Conference
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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.