• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.51-67
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• 2004

A matrix pair $(X_0,\;Y_0)$ is called a Hermitian nonnegative-definite(respectively, positive-definite) solution to the matrix equation $GXG^*\;+\;HYH^*\;=\;C$ with unknown X and Y if $X_{0}$ and $Y_{0}$ are Hermitian nonnegative-definite (respectively, positive-definite) and satisfy $GX_0G^*\;+\;HY_0H^*\;=\;C$. Necessary and sufficient conditions for the existence of at least a Hermitian nonnegative-definite (respectively, positive-definite) solution to the matrix equation are investigated. A representation of the general Hermitian nonnegative-definite (respectively positive-definite) solution to the equation is also obtained when it has such solutions. Two presented examples show these advantages of the proposed approach.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.321-328
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• 2005

We investigate a matrix inequality on Schur complements defined by {1}-generalized inverses, and obtain simultaneously a necessary and sufficient condition under which the inequality turns into an equality. This extends two existing matrix inequalities on Schur complements defined respectively by inverses and Moore-Penrose generalized inverses (see Wang et al. [Lin. Alg. Appl., 302-303(1999)163-172] and Liu and Wang [Lin. Alg. Appl., 293(1999)233-241]). Moreover, the non-uniqueness of $\{1\}$-generalized inverses yields the complicatedness of the extension.

• Investigative Magnetic Resonance Imaging
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• 제11권2호
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• pp.110-118
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• 2007

목적: 확산텐서자기공명영상(DT-MRI: Diffusion Tensor Image)을 이용하여 확산의 주축을 구성하는 세 성분에 대한 고유치 (eigefvalue)의 영상을 구현해 보고자 하였다. 대상 및 방법: 고유치 영상을 구현하기 위해서 3.0 테슬러 MRI(Magnetic Resonance Imaging)를 이용하여 확산텐서영상을 얻었으며, Moore-Penrose pseudo-inverse 방법과 SVD(single value decomposition) 방법을 이용하여 확산 주축을 계산하였다. 이 과정을 픽셀단위로 반복적으로 계산하여 새로운 확산 주축 영상들을 만들었으며, 이 확산 주축 영상들과 분할 비등방성 영상의 관계를 조사하였다. 결과: 확산텐서영상 기법으로 얻어진 확산텐서영상을 이용하여, 세 방향의 확산 주축에 대한 고유치 영상을 구성하였으며, 고유치 영상들과 분할 비등방성 영상을 함께 분석함으로써, 뇌의 해부학적 구조물에 따른 분할 비등방성 값의 차이를 확인할 수 있었다. 또한, 확산 주축에 대한 고유치의 변화에 대한 컴퓨터 모의실험에서, 변화하는 고유치에 따른 분할 비등방성 값의 변동 추이를 알아볼 수 있었다. 그리고 확산 주축의 크기가 비등방성을 좌우하는 것이 아니라, 세 확산 주축의 조합으로 비등방성의 정도를 표현한다는 것을 확인할 수 있었다. 확산 주축 방향의 고유치들을 분리하여 영상화 함으로써, 뇌의 병변에 의한 비등방성의 변화의 원인이 확산 주축의 어떠한 변화에 의해 발생하는 것인지 확인할 수 있을 것으로 기대된다.

• 토지주택연구
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• 제11권2호
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• pp.33-46
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• 2020

As the fastest growing office transaction volume in Korea, there's been a need for development of indicators to accurately diagnose the office capital market. The purpose of this paper is experimentally calculate to the office price index for effective benchmark indices in Seoul. The quantitative methodology used a Case-Shiller Repeat Sales Model (1991), based on actual multiple office transaction dataset with over minimum 1,653 ㎡ from Q3 1999 to 4Q 2019 in the case of 1,536 buildings within Seoul Metropolitan. In addition, the collected historical data and spatial statistical analysis tools were treated with the SAS 9.4 and ArcGIS 10.7 programs. The main empirical results of research are briefly summarized as follows; First, Seoul office price index was estimated to be 344.3 point (2001.1Q=100.0P) at the end of 2019, and has more than tripled over the past two decades. it means that the sales price of office per 3.3 ㎡ has consistently risen more than 12% every year since 2000, which is far above the indices for apartment housing index, announced by the MOLIT (2009). Second, between quarterly and annual office price index for the two-step estimation of the MIT Real Estate Research Center (MIT/CRE), T, L, AL variables have statistically significant coefficient (Beta) all of the mode l (p<0.01). Third, it was possible to produce a more stable office price index against the basic index by using the Moore-Penrose's pseoudo inverse technique at low transaction frequency. Fourth, as an lagging indicators, the office price index is closely related to key macroeconomic indicators, such as GDP(+), KOSPI(+), interest rates (5-year KTB, -). This facts indicate that long-term office investment tends to outperform other financial assets owing to high return and low risk pattern. In conclusion, these findings are practically meaningful to presenting an new office price index that increases accuracy and then attempting to preliminary applications for the case of Seoul. Moreover, it can provide sincerely useful benchmark about investing an office and predicting changes of the sales price among market participants (e.g. policy maker, investor, landlord, tenant, user) in the future.