• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.373-385
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• 2009

An m${\times}$n Boolean matrix A is called regular if there exists an n${\times}$m Boolean matrix X such that AXA = A. We have characterizations of Boolean regular matrices. We also determine the linear operators that strongly preserve Boolean regular matrices.

• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.1-7
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• 2006

In this paper, we investigate bounded matrices over regular rings. We observe that every bounded matrix over a regular ring can be described by idempotent matrices and invertible matrices. Let A, $B{in}M_n(R)$ be bounded matrices over a regular ring R. We prove that $(AB)^d = U(BA)^dU^{-1}$ for some $U{\in}GL_n(R)$.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.497-505
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• 2017

The rank over a finite field of the adjacency matrix of a directed strongly regular graph is studied, with some applications to the construction of linear codes. Three techniques are used: code orthogonality, adjacency matrix determinant, and adjacency matrix spectrum.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1713-1726
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• 2018

We study the one-sided regularity of matrices in upper triangular matrix rings in relation with the structure of diagonal entries. We next consider a ring theoretic condition that ab being regular implies ba being also regular for elements a, b in a given ring. Rings with such a condition are said to be commutative at regular product (simply, CRP rings). CRP rings are shown to be contained in the class of directly finite rings, and we prove that if R is a directly finite ring that satisfies the descending chain condition for principal right ideals or principal left ideals, then R is CRP. We obtain in particular that the upper triangular matrix rings over commutative rings are CRP.

• Korean Journal of Mathematics
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• v.11 no.2
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• pp.155-160
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• 2003

In this paper we shall study the limit of the doubly stochastic matrices obtained from Boolean regular matrices.

• Korean Journal of Mathematics
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• v.7 no.1
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• pp.53-60
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• 1999

We find bounds of eigenvalues of bipartite tournament matrices. We see when bipartite matrices exist and how players and teams of the matrices are evenly ranked. Also, we show that a bipartite tournament matrix can be both regular and normal when and only when it has the same team size.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.207-220
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• 2004

Necessary and sufficient conditions are given for the regularity of block triangular fuzzy matrices. This leads to characterization of idem-potency of a class of triangular Toeplitz matrices. As an application, the existence of group inverse of a block triangular fuzzy matrix is discussed. Equivalent conditions for a regular block triangular fuzzy matrix to be expressed as a sum of regular block fuzzy matrices is derived. Further, fuzzy relational equations consistency is studied.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1333-1338
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• 2018

A ${\ast}-ring$ R is called ${\ast}-regular$ if every principal one-sided ideal of R is generated by a projection. In this note, several characterizations of ${\ast}-regular$ rings are provided. In particular, it is shown that a matrix ring $M_n(R)$ is ${\ast}-regular$ if and only if R is regular and $1+x^*_1x_1+{\cdots}+x^*_{n-1}x_{n-1}$ is a unit for all $x_i$ of R; which answers a question raised in the literature recently.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.401-409
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• 2000

In this paper, we determine the structure of ${\kappa}-potent$ elements and regular elements of the semigroup ${\Omega}_n$of doubly stochastic matrices of order n. In connection with this, we find the structure of the matrices X satisfying the equation AXA = A. From these, we determine a condition of a doubly stochastic matrix A whose Moore-Penrose generalized is also a doubly stochastic matrix.

• The Korean Journal of Applied Statistics
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• v.20 no.2
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• pp.373-385
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• 2007

The solution of the normal equation arising in a general linear model by the least square methods is not unique in general. Conventionally, SAS IML and G-inverse matrices are considered for such problems. In this paper, we provide a systematic solution procedures for SAS IML.