• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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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.

• Kyungpook Mathematical Journal
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• v.28 no.2
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• pp.221-226
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• 1988

Using the method of eigenfunction expantion of self adjoint operators, we establish the necessary and sufficient conditions for a reflection positive generalized matrix kernel to be represented in an integral form. This integral converges in the cosidered spaces.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.6B
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• pp.1123-1133
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• 1999

In this paper, we applied mode matching and generalized scattering matrix methods to three plane mode matching method for analyzing T-junctions. We calculated all scattering matrix elements by only three times and considered several incident modes. By proposed analysis method, we could analyze various waveguide discontinuity structures more conveniently and accurately. Using the stepped T-junction, we would be able to reduce the reflection coefficient at an input port and use it over wider band. Simulated and HFSS data of T-junctions are compared, showing good agreement for scattering matrix elements. Considering step numbers, height, length and position, we extracted for optimum dimensions and equivalent circuit parameters.

• Communications of the Korean Mathematical Society
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• v.16 no.4
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• pp.679-690
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• 2001

Doubly stochastic matrices are n$\times$n nonnegative ma-trices whose row and column sums are all 1. Convex polytope $\Omega$$_{n}$ of doubly stochastic matrices and more generally (R,S), so called transportation polytopes, are important since they form the domains for the transportation problems. A theorem by Birkhoff classifies the extremal matrices of , $\Omega$$_{n}$ and extremal matrices of transporta-tion polytopes (R,S) were all classified combinatorially. In this article, we consider signed version of $\Omega$$_{n}$ and (R.S), obtain signed Birkhoff theorem; we define a new class of convex polytopes (R,S), calculate their dimensions, and classify their extremal matrices, Moreover, we suggest an algorithm to express a matrix in (R,S) as a convex combination of txtremal matrices. We also give an example that a polytope of signed matrices is used as a domain for a decision problem. In this context of finite reflection(Coxeter) group theory, our generalization may also be considered as a generalization from type $A_{*}$ n/ to type B$_{n}$ D$_{n}$. n/.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.40 no.11
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• pp.1-9
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• 2003

The electromagnectic modal analysis method for the multiscreen structure with periodic slot array with including conductor thickness effect is presented. The multiscreen structure is seen to be exactly equivalent to a microwave guide closed by phase-shift walls. From this viewpoint, the entire generalized scattering matrix of the multiscreen structure is calculated by the cascade connection of the scattering matrices obtained by the modal analysis at guide junctions and the transmission matrices of guide region. The present method is verified in comparison with the results calculated by the previous method of moment for single screen structure. As an application example of the present method, the spatial filter having multiscreen structure is designed and the interesting characteristics such as transmission and reflection coefficient versus frequency & angle are investigated.