• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.1
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• pp.85-91
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• 2020

In this parer we express the sufficient conditions under which it is proved that a J-normal irreduciable Hessenberg matrix is tridiagonal and it is also proved that a similar statement exists for J-conjugate normal matrices

• Honam Mathematical Journal
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• v.29 no.1
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• pp.75-81
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• 2007

The Fisher information matrix plays a significant role in statistical inference in connection with estimation and properties of variance of estimators. In this paper, the parameter space of the normal distribution using its Fisher's matrix is defined. The Riemannian curvature and J-divergence to parameter space are calculated.

• Journal of the Korean Statistical Society
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• v.25 no.3
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• pp.393-406
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• 1996

We obtain the general moment of non-central Wishart distribu-tion, using the J-th moment of a matrix quadratic form and the 2J-th moment of the matrix normal distribution. As an example, the second moment and kurtosis of non-central Wishart distribution are also investigated.

• Kyungpook Mathematical Journal
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• v.28 no.1
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• pp.45-50
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• 1988

Circulant and multiblock circulant matrices have many important applications, and therefore their inverses are of considerable interest. A simple recursive algorithm is presented to compute the inverse of a multiblock circulant matrix. The algorithm only uses complex variables, roots of unity and normal matrix/vector operations.

• Proceedings of the KIEE Conference
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• 1989.07a
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• pp.233-236
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• 1989

This paper deals with the expert system using network configuration and input information composed of protective relays and tripped circuit breakers. This system has knowlegebase independent on network dimension because network representation consists of the type of the matrix. Therefore, the knowlege of network representation is simplified, the space of knowlege is reduced, the addition of facts to the knowlege is easy and the expansion of facts is possible. In this paper, the network representation is defined to system matrix. This expert system based on the system matrix diagnoses normal, abnormal operations of protective devices as well as possible fault sections. The brach and bound search technique is used: breadth first technique mixed with depth first technique of primitive PROLOG search technique. This system will be used for real time operations. This expert system obtaines the solution using the pattern matching in working memory without no listing approach for rule control. This paper is written in PROLOG, the A.I. language.

• Journal of Korean Society of Forest Science
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• v.67 no.1
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• pp.52-59
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• 1984

A Gentan probability q(j) is the probability that a newly planted forest will be felled at age-class j. A future change in growing stock and yield of the forests can be predicted by means of this probability. On the other hand a state of the forests is described in terms of an n-vector whose components are the areas of each age-class. This vector, called age-class vector, flows in a n-1 dimensional simplex by means of $n{\times}n$ matrices, whose components are the age-class transition probabilities derived from the Gentan probabilities. In the simplex there exists a fixed point, into which an arbitrary forest age vector sinks. Theoretically this point means a normal state of the forest. To each age-class-transition matrix there corresponds a single normal state; this means that there are infinitely many normal states of the forests.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.603-613
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• 2013

In 2009, Zheng and Miao [B. Zheng and S.-X. Miao, Two new modified Gauss-Seidel methods for linear system with M-matrices, J. Comput. Appl. Math. 233 (2009), 922-930] considered the modified Gauss-Seidel method for solving M-matrix linear system with the preconditioner $P_{max}$. In this paper, we consider the modified Gauss-Seidel method for solving the linear system with the generalized preconditioner $P_{max}({\alpha})$, and study its convergent properties when the coefficient matrix is an H-matrix. Numerical experiments are performed with different examples, and the numerical results verify our theoretical analysis.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.493-506
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• 2017

In this paper, we define the modulus of n-dimensional U-flatness as the determinant of an $(n+1){\times}(n+1)$ matrix. The properties of the modulus are investigated and the relationships between this modulus and other geometric parameters of Banach spaces are studied. Some results on fixed point theory for non-expansive mappings and normal structure in Banach spaces are obtained.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1273-1283
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• 2019

In matrix analysis, the Wielandt-Mirsky conjecture states that $$dist({\sigma}(A),{\sigma}(B)){\leq}{\parallel}A-B{\parallel}$$ for any normal matrices $A,B{\in}{\mathbb{C}}^{n{\times}n}$ and any operator norm ${\parallel}{\cdot}{\parallel}$ on $C^{n{\times}n}$. Here dist(${\sigma}(A),{\sigma}(B)$) denotes the optimal matching distance between the spectra of the matrices A and B. It was proved by A. J. Holbrook (1992) that this conjecture is false in general. However it is true for the Frobenius distance and the Frobenius norm (the Hoffman-Wielandt inequality). The main aim of this paper is to study the Hoffman-Wielandt inequality and some weaker versions of the Wielandt-Mirsky conjecture for matrix polynomials.

• Journal of the Korean Mathematical Society
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• v.53 no.3
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• pp.519-532
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• 2016

The zero-divisor graph of a noncommutative ring R, denoted by ${\Gamma}(R)$, is a graph whose vertices are nonzero zero-divisors of R, and there is a directed edge from a vertex x to a distinct vertex y if and only if xy = 0. Let $R=M_2(F_q)$ be the $2{\times}2$ matrix ring over a finite field $F_q$. In this article, we investigate the automorphism group of ${\Gamma}(R)$.