• Kyungpook Mathematical Journal
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• v.46 no.4
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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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• v.13 no.5
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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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• v.22 no.4
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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.

• Journal of Information Technology Services
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• v.6 no.1
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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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• v.41 no.6
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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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• v.15 no.2
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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.

• Journal of Korea Society of Industrial Information Systems
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• v.12 no.2
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• pp.68-78
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• 2007

D-class is defined as a set of equivalent $n{\times}n$ boolean matrices according to a given equivalence relation. The D-class computation requires the multiplication of three boolean matrices for each of all possible triples of $n{\times}n$ boolean matrices. However, almost all the researches on boolean matrices focused on the efficient multiplication of only two boolean matrices and a few researches have recently been shown to deal with the multiplication of all boolean matrices. The paper suggests a mathematical theory that enables the efficient multiplication for all possible boolean matrix triples and the efficient computation of all D-classes, and discusses algorithms designed with the theory and their execution results.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.3A
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• pp.412-416
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• 2000

Hadamard matrices are known to be important in designing of the orthogonal codes. in this paper we propose generalized Sylvester construction for Hadamard matrices. We prove it and give an example for the case of Hadamard matrices of order16.

• Journal of applied mathematics & informatics
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• v.7 no.2
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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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• v.2 no.3
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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.