• 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.

• Korean Journal of Mathematics
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• v.22 no.3
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• pp.443-454
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• 2014

In this paper, we give linearization of generalized Fi-bonacci sequences {$g_n$} and {$q_n$}, respectively, defined by Eq.(5) and Eq.(6) below and use this result to give the matrix form of the nth power of a companion matrix of {$g_n$} and {$q_n$}, respectively. Then we re-prove the Cassini's identity for {$g_n$} and {$q_n$}, respectively.

• Honam Mathematical Journal
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• v.38 no.4
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• pp.725-738
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• 2016

In this paper, the explicit determinants of the circulant and negacyclic matrix involving Tetranacci sequence $M_n$ and Companion-Tetranacci sequence $K_n$ are expressed by using only Tetranacci sequence $M_n$ and Companion-Tetranacci sequence $K_n$. Also euclidean norms and spectral norms of circulant and negacyclic matrices have been obtained.

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.845-858
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• 2021

We present new bounds for the numerical radius of bounded linear operators and 2 × 2 operator matrices. We apply upper bounds for the numerical radius to the Frobenius companion matrix of a complex monic polynomial to obtain new estimations for the zeros of that polynomial. We also show with numerical examples that our new estimations improve on the existing estimations.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.505-513
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• 2019

In this paper, we study orthanogonal polynomials by looking at their comrade matrices and reachability matrices. First, we focus on the algebraic structure that is exhibited by comrade matrices. Then, we explain some properties of this algebraic structure which helps us to find a connection between comrade matrices and reachability matrices. In the last section, we use this connection to determine the determinant, eigenvalues, and eigenvectors of these matrices. Finally, we derive a factorization for det R(A, x), where R(A, x) is the reachability matrix for a comrade matrix A and x is a vector of indeterminates.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.40 no.4
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• pp.646-652
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• 2015

In this paper, the system-level performance is evaluated for the feedback scheme on the pre-coding matrix index (PMI) and channel quality indication (CQI), which are required for user selection in the multi-user MIMO system. Our analysis demonstrates that the number of users, the number of selected users, and codebook size are the key factors that govern the performance of the best companion grouping (BCG)-based user scheduling. Accordingly, we have confirmed that the probability of forming the co-scheduled user group is determined by these factors, which implies that the number of PMI's and codebook size can be dynamically determined so as to maximize the average system throughput as the number of users varies in the cell.

• Design Convergence Study
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• v.16 no.6
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• pp.137-152
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• 2017

This research aims to develop the companion robot experience design for elderly in korea based on needs-function deploy matrix of robot and emotion expression research of robot in multimodal interaction. First, Elder users' main needs were categorized into 4 groups based on ethnographic research. Second, the functional elements and physical actuators of robot were mapped to user needs in function- needs deploy matrix. The final UX design prototype was implemented with a robot type that has a verbal non-touch multi modal interface with emotional facial expression based on Ekman's Facial Action Coding System (FACS). The proposed robot prototype was validated through a user test session to analyze the influence of the robot interaction on the cognition and emotion of users by Story Recall Test and face emotion analysis software; Emotion API when the robot changes facial expression corresponds to the emotion of the delivered information by the robot and when the robot initiated interaction cycle voluntarily. The group with emotional robot showed a relatively high recall rate in the delayed recall test and In the facial expression analysis, the facial expression and the interaction initiation of the robot affected on emotion and preference of the elderly participants.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.54 no.2
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• pp.67-72
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• 2005

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

• 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.

• Proceedings of the KIEE Conference
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• summer
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• pp.342-344
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• 2004

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