• Kyungpook Mathematical Journal
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• 제46권4호
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• pp.581-589
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• 2006

We characterize the linear operators which preserve the factor rank of integer matrices. That is, if $\mathcal{M}$ is the set of all $m{\times}n$ matrices with entries in the integers and min($m,n$) > 1, then a linear operator T on $\mathcal{M}$ preserves the factor rank of all matrices in $\mathcal{M}$ if and only if T has the form either T(X) = UXV for all $X{\in}\mathcal{M}$, or $m=n$ and T(X)=$UX^tV$ for all $X{\in}\mathcal{M}$, where U and V are suitable nonsingular integer matrices. Other characterizations of factor rank-preservers of integer matrices are also given.

• Journal of Communications and Networks
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• 제13권5호
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• pp.449-455
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• 2011

Inspired by fast Jacket transforms, we propose simple factorization and construction algorithms for the M-dimensional discrete Fourier transform (DFT) matrices underlying generalized Chinese remainder theorem (CRT) index mappings. Based on successive coprime-order DFT matrices with respect to the CRT with recursive relations, the proposed algorithms are presented with simplicity and clarity on the basis of the yielded sparse matrices. The results indicate that our algorithms compare favorably with the direct-computation approach.

• Communications for Statistical Applications and Methods
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• 제22권4호
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• pp.321-331
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• 2015

The K-means clustering algorithm is a popular and widely used method for clustering. For covariance matrices, we consider a geodesic clustering algorithm based on the K-means clustering framework in consideration of symmetric positive definite matrices as a Riemannian (non-Euclidean) manifold. This paper considers a geodesic clustering algorithm for data consisting of symmetric positive definite (SPD) matrices, utilizing the Riemannian geometric structure for SPD matrices and the idea of a K-means clustering algorithm. A K-means clustering algorithm is divided into two main steps for which we need a dissimilarity measure between two matrix data points and a way of computing centroids for observations in clusters. In order to use the Riemannian structure, we adopt the geodesic distance and the intrinsic mean for symmetric positive definite matrices. We demonstrate our proposed method through simulations as well as application to real financial data.

• 한국IT서비스학회지
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• 제6권1호
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• pp.151-158
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• 2007

D-class computation requires multiplication of three Boolean matrices for each of all possible triples of $n{\times}n$ Boolean matrices and search for equivalent $n{\times}n$ Boolean matrices according to a specific equivalence relation. It is easy to see that even multiplying all $n{\times}n$ Boolean matrices with themselves shows exponential time complexity and D-Class computation was left an unsolved problem due to its computational complexity. The vector-based multiplication theory shows that the multiplication of three Boolean matrices for each of all possible triples of $n{\times}n$ Boolean matrices can be done much more efficiently. However, D-Class computation requires computation of equivalent classes in addition to the efficient multiplication. The paper discusses a theory and an algorithm for efficient D-class computation, and shows execution results of the algorithm.

• Journal of applied mathematics & informatics
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• 제41권6호
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• pp.1181-1191
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• 2023

This paper investigates Young inequalities for matrices, a problem closely linked to operator theory, mathematical physics, and the arithmetic-geometric mean inequality. By obtaining new inequalities for unitarily invariant norms, we aim to derive a fresh Young inequality specifically designed for matrices.To lay the foundation for our study, we provide an overview of basic notation related to matrices. Additionally, we review previous advancements made by researchers in the field, focusing on Young improvements.Building upon this existing knowledge, we present several new enhancements of the classical Young inequality for nonnegative real numbers. Furthermore, we establish a matrix version of these improvements, tailored to the specific characteristics of matrices. Through our research, we contribute to a deeper understanding of Young inequalities in the context of matrices.

• East Asian mathematical journal
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• 제15권2호
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• pp.223-232
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• 1999

In this paper, we give the upper bound of determinants of (0,1)-tridiagonal matrices and we show that the (0,1)-tridiagonal matrices which have maximal determinant are sign-nonsingular.

• 한국산업정보학회논문지
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• 제12권2호
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• pp.68-78
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• 2007

D-클래스는 주어진 동치관계(equivalence relation)에 있는 $n{\times}n$ 불리언 행렬의 집합으로 정의된다. D-클래스 계산은 $n{\times}n$ 불리언 행렬의 전체 집합을 대상으로 이 집합에서 조합할 수 있는 모든 세 불리언 행렬 사이의 곱셈을 요구한다. 그러나 불리언 행렬에 대한 대부분의 연구는 단지 두 개의 불리언 행렬에 대한 효율적인 곱셈에 집중되었으며 모든 불리언 행렬 사이의 곱셈에 대한 연구는 최근에야 소수가 보이고 있다. 본 논문은 모든 세 개의 불리언 행렬 곱셈과 모든 D-클래스를 보다 효율적으로 계산할 수 있는 이론을 제시하고 이를 적용한 알고리즘과 실행결과에 대하여 논한다.

• 한국통신학회논문지
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• 제25권3A호
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• pp.412-416
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• 2000

하다마드 행렬은 직교부호를 설계함에 있어서 매우 중요한 행렬이다. 본 논문에서는 하다마드 행렬을 구성하는 실베스터(Sylvester) 방식의 새로운 일반화된 방법을 소개하고 이를 증명한 후, 크기 16에서 예를 들어 설명한다. 이 방법을 사용하면 서로 비동치관계에 있는 다양한 종류의 하다마드 행렬을 쉽게 생성할 수 있다.

• Journal of applied mathematics & informatics
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• 제7권2호
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• pp.665-671
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• 2000

A matrix whose entries consist of the symbols +.- and 0 is called a sign pattern matrix . In 1994 , Eschenbach gave a graph theoretic characterization of irreducible sign idempotent pattern matrices. In this paper, we give a characterization of reducible sign idempotent matrices. We show that reducible sign idempotent matrices, whose digraph is contained in an irreducible sign idempotent matrix, has all nonnegative entries up to equivalences. this extend the previous result.

• The Korean Journal of Ceramics
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• 제2권3호
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• pp.142-146
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• 1996

The molten carbonate fuel cell matrices, which are usually made of high surface, fine particle size ${\gamma}-LiAlO_2$ are reinforced with coarse particles of the same material and alumina fibers. An the effects of reinforcing materials on pore characteristics, sintering properties and mechanical properties of the matrices are examined.Among the matrices examined, the highest mechanical reinforcement has been achieved in the one containing 10 wt.% coarse particles and 20 wt.% alumina fibers.