• Journal of applied mathematics & informatics
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• 제8권2호
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• pp.651-658
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• 2001

The projection matrix plays an important role in the linear model theory. In this paper we derive an algebraic relationship between the projection matrices of submatrices of the design matrix. Using this relationship we can easily obtain the projection matrices of any submatrices of the design matrix. Also we show that every projection matrix can be obtained as a linear combination of Kronecker products of identity matrices and matrices with all elements equal to 1.

• 정보저장시스템학회논문집
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• 제3권3호
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• pp.126-128
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• 2007

일반적으로 주어진 하나의 H matrix 로 다수의 코드율을 가지는 코드화가 가능하다. 하지만 Low Density Parity Check(LDPC) 코드의 H matrix는 H matrix 내의 1의 개수와 위치에 따라 그 성능이 달라짐으로 해서 하나의 H matrix로 다수의 코드율을 대응하기 위한 설계 방법이 요구된다. H matrix 의 성능은 일반적으로 girth나 minimum distance에 의해 좌우되고 H matrix의 1의 위치에 따라 달라진다. 본 논문에서는 H matrix의 girth 와 minimum distance에 입각한 다수 개의 코드율이 대응 가능한 LDPC code의 H matrix 설계 방법을 제시하고자 한다. 이렇게 함으로써 하나의 H matrix로 다수의 코드율에 따른 각각의 성능을 일정 수준 이상 유지하는 multi-rate LDPC code가 가능하다.

• 한국전자통신학회논문지
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• 제12권1호
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• pp.101-108
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• 2017

양자게이트 행렬은 치수가 r, 제어상태벡터 수가 n 및 표적상태벡터 수가 1인 경우에 $r^{n+1}{\times}r^{n+1}$ 차원 행렬이므로 n 증가에 따른 행렬 크기는 지수 함수적 증가 특성을 갖는다. 만약 제어상태벡터의 경우 수가 $2^n$이라면 $2^n-1$ 경우는 입력이 출력에 보전되는 단위행렬의 항등연산이고, 오직 한 개의 제어상태벡터 연산만이 표적상태벡터에 대한 유니터리 연산이다. 본 논문은 행렬차원 증가에 결정적 기여를 하는 $2^n-1$개의 단위행렬 연산을 한 동작의 산술멱승 연산으로 대체할 수 있는 새로운 함수 임베딩 방법을 제안한다. 제안한 함수 임베딩 방법은 다치 임계값을 갖는 2진 리터럴 스위치를 사용하므로 범용 하이브리드 MCU 게이트를 $r{\times}r$ 유니터리 행렬로 실현할 수 있다.

• 대한수학회지
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• 제48권1호
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• pp.33-48
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• 2011

The notion of the generalized Fibonacci matrix $\mathcal{F}_n^{(a,b,s)}$ of type s, whose nonzero elements are generalized Fibonacci numbers, is introduced in the paper [23]. Regular case s = 0 is investigated in [23]. In the present article we consider singular case s = -1. Pseudoinverse of the generalized Fibonacci matrix $\mathcal{F}_n^{(a,b,-1)}$ is derived. Correlations between the matrix $\mathcal{F}_n^{(a,b,-1)}$ and the Pascal matrices are considered. Some combinatorial identities involving generalized Fibonacci numbers are derived. A class of test matrices for computing the Moore-Penrose inverse is presented in the last section.

• Bulletin of the Korean Chemical Society
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• 제35권12호
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• pp.3482-3488
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• 2014

Matrix-induced mass bias and its effect on the accuracy of isotope ratio measurements have been examined for a quadrupole-based inductively coupled plasma-mass spectrometer (Q ICP-MS). Matrix-induced mass bias effect was directly proportional to % mass difference, and its magnitude varied for element and nebulizer flow rate. For a given element and conditions in a day, the effect was consistent. The isotope ratio of Cd106/Cd114 under $200{\mu}g\;g^{-1}$ U matrix deviated from the natural value significantly by 3.5%. When Cd 111 and Cd114 were used for the quantification of Cd with isotope dilution (ID) method, the average of differences between the calculated and measured concentrations was -0.034% for samples without matrix ($0.076{\mu}g\;g^{-1}$ to $0.21{\mu}g\;g^{-1}$ for the period of 6 months). However, the error was as large as 1.5% for samples with $200{\mu}g\;g^{-1}$ U. The error in ID caused by matrix could be larger when larger mass difference isotopes are used.

• 대한수학회지
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• 제50권1호
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• pp.127-136
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• 2013

The term rank of a matrix A is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we obtain a characterization of linear transformations that preserve term ranks of matrices over antinegative semirings. That is, we show that a linear transformation T from a matrix space into another matrix space over antinegative semirings preserves term rank if and only if T preserves any two term ranks $k$ and $l$.

• 대한수학회지
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• 제55권2호
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• pp.327-342
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• 2018

In this paper, a homotopy continuation method for obtaining the unique Hermitian positive definite solution of the nonlinear matrix equation $X-{\sum_{i=1}^{m}}A^{\ast}_iX^{-p_i}A_i=I$ with $p_i$ > 1 is proposed, which does not depend on a good initial approximation to the solution of matrix equation.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.59-72
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• 2005

We study convergence of symmetric multisplitting method associated with many different multisplittings for solving a linear system whose coefficient matrix is a symmetric positive definite matrix which is not an H-matrix.

• 한국통신학회논문지
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• 제17권7호
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• pp.739-748
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• 1992

스트라이프 구조를 이용하여 대형 스파스 선형 방정식을 해석하는 CGM 반복 씨스톨릭 알고리즘을 제시하고, 이를 씨스톨릭 어레이로 구현했다. 메트릭스 A를 상삼각 행렬과 대각선행렬, 하삼각 행렬로 나누어서 이들이 별개의 선형 어레이에 의해서 병행적으로 실행되도록 했다. 따라서 1개의 선형 어레이를 사용했을 때보다도 실행시간이 대략 1/2로 단축되며, 스트라이프 구조를 이용하므로서 불규칙하게 분포된 스파스메트릭스의 연산을 효율적으로 할 수 있다.

• 한국세라믹학회지
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• 제31권4호
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• pp.375-380
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• 1994

Matrices retaining electrolyte in phosphoric acid fuel cell were prepared with SiC to SiC whisker mixing ratios of 1:0.5, 1:1, 1:1.5, 1:2, 1:3 by tape casting method. When viscosity of the slurry was 5.9 poise and the SiC to SiC whisker mixing ratios were 1:1, 1:1.5, 1:2, the ranges of porosity, acid absorbency and bubble pressure were 80~90%, 2.5~6 and 700~2200 mmH2O, respectively. Those ranges are acceptable for a practical electrolyte-retaining matrix. With increasing the mixing ratio of SiC whisker to SiC, the porosity and the vol.% of large pores in the main pore size distribution which is between 1 and 10 ${\mu}{\textrm}{m}$, increased rapidly. Impedance spectroscopy was measured to know characteristics of matrix inside and contact region of matrix to catalyst layer. When the SiC to SiC whisker mixing ratio was 1:2, hydrogen ions were transported in the matrix most effectively because of high ionic conductivity and low activation energy due to high acid absorbency in spite of high interfacial resistance. The cell current density of the cell made using the matrix was 220 mA/$\textrm{cm}^2$ at 0.7 V.