• 대한수학회논문집
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• 제35권2호
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• pp.487-497
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• 2020

In this paper, we establish a complex matrix representation of the Clifford algebra Cℓ_p,q. The size of our representation is significantly smaller than the size of the elements in L_p,q(ℝ). Additionally, we give detailed information about the spectrum of the constructed matrix representation.

• Journal of applied mathematics & informatics
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• 제39권1_2호
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• pp.125-131
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• 2021

In the paper, we investigate the representation of the numerical range W(An) for the 2 × 2 complex matrix A, in terms of the numerical range W(A) of the matrix A, and the elements of A or the eigenvalue of A.

• 대한수학회논문집
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• 제34권4호
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• pp.1135-1143
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• 2019

The matrix representation of the Toeplitz operator on the Hardy space with respect to a generalized orthonormal basis for the space of square integrable functions associated to a bounded simply connected region in the complex plane is completely computed in terms of only the Szegő kernel and the Garabedian kernels.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.81-96
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• 2004

The level-m scaled circulant factor matrix over the complex number field is introduced. Its diagonalization and spectral decomposition and representation are discussed. An explicit formula for the entries of the inverse of a level-m scaled circulant factor matrix is presented. Finally, an algorithm for finding the inverse of such matrices over the quaternion division algebra is given.

• 대한수학회지
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• 제52권6호
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• pp.1271-1286
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• 2015

An operator T on a complex Hilbert space H is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for H. In this paper, we study skew symmetric operators with eigenvalues. First, we provide an upper-triangular operator matrix representation for skew symmetric operators with nonzero eigenvalues. On the other hand, we give a description of certain skew symmetric triangular operators, which is based on the geometric relationship between eigenvectors.

• 대한음성학회지:말소리
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• 제29_30호
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• pp.43-60
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• 1995

Standard generative phonologists assumed that there were no orders or hierarchies among distinctive features. This means that the distinctive features which make up a segment are independent and unordered. The unordered linear matrix cannot explain phonological phenomena such as complex segments as hierarchical representation does neatly. The hierarchical feature representation theory which embodies the concept of multi-tiered phonological representation organizes distinctive features in the appearance of hierarchical dominance. This paper aims to show how we can solve some problems of the linear feature representation. As regard underlying representation the theory of underspecification is discussed. I propose a feature hierarchy similar to that of Sagey(1986) but slightly different. I show English consonantal assimilation in feature hierarchical model compared with that of feature changing theory of linear representation.

• 대한수학회보
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• 제46권3호
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• pp.511-519
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• 2009

A matrix $P{\in}\mathbb{C}^{n{\times}n}$ is called a generalized reflection matrix if $P^*$ = P and $P^2$ = I. An $n{\times}n$ complex matrix A is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix P if A = PAP (A = -PAP). It is well-known that the reflexive and anti-reflexive matrices with respect to the generalized reflection matrix P have many special properties and widely used in engineering and scientific computations. In this paper, we give new necessary and sufficient conditions for the existence of the reflexive (anti-reflexive) solutions to the linear matrix equation AXB + CY D = E and derive representation of the general reflexive (anti-reflexive) solutions to this matrix equation. By using the obtained results, we investigate the reflexive (anti-reflexive) solutions of some special cases of this matrix equation.

• 대한산업공학회지
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• 제24권2호
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• pp.185-197
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• 1998

Engineering design involves the specification of many variables that define a product, how it is made, and how it behaves. Before some variables can be determined, other variables must first be known or assumed. This fact implies a precedence order of the variables, and of the tasks of determining these variable consequently. Moreover, design of complex systems may involve a large number of design activities. In this paper, the activity-activity incidence matrix is considered as a representation of design activity analysis which mainly focuses on the precedence constraint. In order to analyze the activity-activity incidence matrix, a heuristic algorithm is proposed, which transforms an activity-activity, parameter-formula, and parameter-parameter incidence matrix into a lower triangular form. The analysis of the structured matrices can not only significantly reduce the overall project complexity by reorganizing few critical tasks in practice, but also aims at obtaining shorter times considering the solution structure by exploring concurrency.

• Smart Structures and Systems
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• 제15권1호
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• pp.81-97
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• 2015

Recently, a new output-only modal identification method based on time-frequency independent component analysis (ICA) has been developed by the authors and shown to be useful for even highly-damped structures. In many cases, it is of interest to identify the complex modes of structures with non-proportional damping. This study extends the time-frequency ICA based method to a complex ICA formulation for output-only modal identification of non-proportionally-damped structures. The connection is established between complex ICA model and the complex-valued modal expansion with sparse time-frequency representation, thereby blindly separating the measured structural responses into the complex mode matrix and complex-valued modal responses. Numerical simulation on a non-proportionally-damped system, laboratory experiment on a highly-damped three-story frame, and a real-world highly-damped base-isolated structure identification example demonstrate the capability of the time-frequency complex ICA method for identification of structures with complex modes in a straightforward and efficient manner.

• 제어로봇시스템학회논문지
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• 제15권7호
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• pp.742-752
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• 2009

Engineering design involves the specification of many variables that define a product, how it is made, and how it behaves applied to computer, communication and control fields. Before some variables can be determined, other variables must first be known or assumed. This fact implies a precedence order of the variables, and of the tasks of determining these variables consequently. Moreover, design of complex systems may involve a large number of design activities. In this paper, the activity-activity incidence matrix is considered as a representation of design activity analysis which mainly focuses on the precedence constraint with an object of doing IDEF3 in process-centered view. In order to analyze the activity-activity incidence matrix, a heuristic algorithm is proposed, which transforms an activity-activity, parameter-formula, and parameter-parameter incidence matrix into a lower triangular form. The analysis of the structured matrices can not only significantly reduce the overall project complexity by reorganizing few critical tasks in practice, but also aims at obtaining shorter times considering the solution structure by exploring concurrency.