• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제3권1호
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• pp.43-53
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• 1999

A real $m{\times}n$ matrix A is called an L-matrix if every matrix in its qualitative class has linearly independent rows. Since the number of the sign pattern matrices of the given size is finite, we can list all patterns lexicographically. In [2], a necessary and sufficient condition for a matrix to be an L-matrix was given. We presented an algorithm which decides whether the given matrix is an L-matrix or not. In this paper, we develope an algorithm and C-program which will determine whether a given matrix is an L-matrix or not, or an SNS-matrix or not. In addition, we have extended our algorithm to be able to classify sign-pattern matrices, and to find barely L-matrices from a given matrix and to list all $m{\times}n$ L-matrices.

• 품질경영학회지
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• 제42권2호
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• pp.221-234
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• 2014

Purpose: The Purpose of this study is to develop a model for predicting agent churn group in the cosmetics industry. We develope two models, pattern model and matrix model, which are compared regarding the prediction accuracy of churn agents. Finally, we try to conclude if there is statistically significant difference between two models by empirical study. Methods: We develop two models using the part of RFM(Recency, Frequency, Monetary) method which is one of customer segmentation method in traditional CRM study. In order to ensure which model can predict churn agents more precisely between two models, we used CRM data of cosmetics company A in China. Results: Pattern model and matrix model have been developed. we find out that there is statistically significant differences between two models regarding the prediction accuracy. Conclusion: Pattern model and matrix model predict churn agents. Although pattern model employed the trend of monetary mount for six months, matrix model that used the amount of sales per month and the duration of the employment is better than pattern model in prediction accuracy.

• 대한수학회보
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• 제56권2호
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• pp.305-318
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• 2019

A sign pattern is a matrix whose entries belong to the set {+, -, 0}. An n-by-n sign pattern ${\mathcal{A}}$ is said to allow an eventually positive matrix or be potentially eventually positive if there exist at least one real matrix A with the same sign pattern as ${\mathcal{A}}$ and a positive integer $k_0$ such that $A^k>0$ for all $k{\geq}k_0$. Identifying the necessary and sufficient conditions for an n-by-n sign pattern to be potentially eventually positive, and classifying the n-by-n sign patterns that allow an eventually positive matrix are two open problems. In this article, we focus on the potential eventual positivity of broom sign patterns. We identify all the minimal potentially eventually positive broom sign patterns. Consequently, we classify all the potentially eventually positive broom sign patterns.

• 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.

• 대한수학회논문집
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• 제10권3호
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• pp.561-573
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• 1995

A matrix whose entries consist of the symbols +, - and 0 is called a sign pattern matrix. In [1], a graph theoretic characterization of sign idempotent pattern matrices was given. A question was given for the sign patterns which allow idempotence. We characterized the sign patterns which allow idempotence in the sign idempotent pattern matrices.

• 응용통계연구
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• 제2권1호
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• pp.54-64
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• 1989

Kurkjian 과 Zelen(1963)에 의해 조화행렬에서 행결합 행렬의 특성에 관계된 성질(Property) A가 제안되었다. 한편으로 Paik(1985)은 조화행렬이 블럭행렬로 분할되고, 분할된 블럭행렬간, 블럭행렬내에서 각각 순환하는 다중순환형식행렬을 갖는 경우를 정의하고, Paik(1985)은 이러한 특성을 갖는 계획을 성질 C라 하였다. 본 논문에서는 다중순환형식행렬을 갖는 조화행렬의 구조에 의하여 불완비블럭계획을 분류하였으며 분류의 목적은 축소된정규방정식의 해와 배치계획을 쉽게 하는데 있다.

• Journal of applied mathematics & informatics
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• 제10권1_2호
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• pp.353-360
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• 2002

In this paper we study when a sign pattern matrix A and a sign pattern vector b have the property that the convex hull of the columns of each matrix with sign pattern A contains a vector with sign pattern b. This study generalizes the notion of sign central matrices.

• 호남수학학술지
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• 제28권3호
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• pp.333-342
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• 2006

We denote by Q(A) the set of all matrices with the same sign pattern as A. A matrix A is an SN-matrix provided there exists a set S of sign patterns such that the set of sign patterns of vectors in the null-space of A is S, for each A ${\in}$ Q(A). We have a characterization of an SN-matrix related with L-matrix and we analyze the structure of an SN-matrix.

• 대한수학회지
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• 제36권3호
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• pp.469-487
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• 1999

Sign patterns of idempotent matrices, especially symmetric idempotent matrices, are investigated. A number of fundamental results are given and various constructions are presented. The sign patterns of symmetric idempotent matrices through order 5 are determined. Some open questions are also given.

• 대한수학회논문집
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• 제13권3호
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• pp.465-473
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• 1998

A real m $\times$ n matrix A is semipositive (SP) if there is a vector x $\geq$ 0 such that Ax > 0, inequalities being entrywise. A is minimally semipositive (MSP) if A is semipositive and no column deleted submatrix of A is semipositive. We give a necessary and sufficient condition for the sign pattern matrix with n positive entries to be minimally semipositive.