• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제4권1호
• /
• pp.109-119
• /
• 2000

It was shown that if Q is a fully indecomposable $n{\times}n$ orthogonal matrix then Q has at least 4n-4 nonzero entries in 1993. In this paper, we show that for each integer p with $4n-4{\leq}p{\leq}n^2$, there exist a fully indecomposable $n{\times}n$ orthogonal matrix with exactly p nonzero entries. Furthermore, we obtain a method of construction of a fully indecomposable $n{\times}n$ orthogonal matrix which has exactly 4n-4 nonzero entries. This is a part of the study in sparse matrices.

• 대한수학회보
• /
• 제43권3호
• /
• pp.619-626
• /
• 2006

Let m be any positive integer, R be a ring with identity, $M_m(R)$ be the matrix ring of all m by m matrices eve. R and $G_m(R)$ be the multiplicative group of all n by n nonsingular matrices in $M_m(R)$. In this pape., the following are investigated: (1) for any pairwise coprime ideals ${I_1,\;I_2,\;...,\;I_n}$ in a ring R, $M_m(R/(I_1{\cap}I_2{\cap}...{\cap}I_n))$ is isomorphic to $M_m(R/I_1){\times}M_m(R/I_2){\times}...{\times}M_m(R/I_n);$ and $G_m(R/I_1){\cap}I_2{\cap}...{\cap}I_n))$ is isomorphic to $G_m(R/I_1){\times}G_m(R/I_2){\times}...{\times}G_m(R/I_n);$ (2) In particular, if R is a finite ring with identity, then the order of $G_m(R)$ can be computed.

• 한국전자통신학회논문지
• /
• 제6권2호
• /
• pp.193-198
• /
• 2011

행렬들 중 그것의 성분으로 부호인 + 와 0 만을 갖는 행렬을 우리는 비음인 부호화 행렬이라 한다. 또한 비음인 부호화 행렬 A가 그것과 같은 부호를 갖는 실수 정규행렬 B가 존재하면 정규성을 허용한다고 한다. 본 논문은 참고문헌[1] 에서 밝힌 형태와 다른 특별한 형태를 조사했고, 실수 행렬 중 비음인 정규행렬을 구성하는 흥미로운 방법을 제공했다.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제21권2호
• /
• pp.121-128
• /
• 2014

The Boolean rank of a nonzero m $m{\times}n$ Boolean matrix A is the least integer k such that there are an $m{\times}k$ Boolean matrix B and a $k{\times}n$ Boolean matrix C with A = BC. In 1984, Beasley and Pullman showed that a linear operator preserves the Boolean rank of any Boolean matrix if and only if it preserves Boolean ranks 1 and 2. In this paper, we extend this characterization of linear operators that preserve the Boolean ranks of Boolean matrices. We show that a linear operator preserves all Boolean ranks if and only if it preserves two consecutive Boolean ranks if and only if it strongly preserves a Boolean rank k with $1{\leq}k{\leq}min\{m,n\}$.

• 한국통신학회논문지
• /
• 제25권10A호
• /
• pp.1560-1565
• /
• 2000

Over an additive abelian group G of order g and for a given positive integer λ, a generalized Hadamard matrix GF(g,λ) is defined as a gλ$\times$gλ matrix [h(i,j)] where 1$\leq$i$\leq$gλ,1$\leq$j$\leq$gλ, such that every element of G appears exactly λ times in the list h(i$_1$,1)-h(i$_2$,1), h(i$_1$,2)-h(i$_2$,2),...,h(i$_1$,gλ)-h(i$_2$, gλ) for any i$\neq$j. In this paper, we propose a new method of expanding a GH(\ulcorner,λ$_1$) = B = \ulcorner over G by replacing each of its m-tuple \ulcorner with \ulcorner GH(g,λ$_2$) where m=gλ$_2$. We may use \ulcornerλ$_1$(not necessarily all distinct) GH(g,λ$_2$)'s for the substitution and the resulting matrix is defined over the group of order g.

• 대한수학회논문집
• /
• 제34권2호
• /
• pp.401-414
• /
• 2019

Let ${\mathcal{F}}$ denote an algebraically closed field with characteristic not two. Fix an integer $d{\geq}3$, let $Mat_{d+1}({\mathcal{F}})$ denote the ${\mathcal{F}}$-algebra of $(d+1){\times}(d+1)$ matrices with entries in ${\mathcal{F}}$. An ordered pair of matrices A, $A^*$ in $Mat_{d+1}({\mathcal{F}})$ is said to be LB-TD form whenever A is lower bidiagonal with subdiagonal entries all 1 and $A^*$ is irreducible tridiagonal. Let A, $A^*$ be a Leonard pair in $Mat_{d+1}({\mathcal{F}})$ with fundamental parameter ${\beta}=2$, with this assumption there are four families of Leonard pairs, Racah, Hahn, dual Hahn, Krawtchouk type. In this paper we show from these four families only Racah and Krawtchouk have LB-TD form.

• 대한수학회논문집
• /
• 제15권1호
• /
• pp.29-36
• /
• 2000

The T-ideal of F(X) generated by $x^{n}$ for all x $\in$ X, is generated also by the symmetric polynomials. For each symmetric poly-nomial, there corresponds one row of the incidence matrix. Finding the nilpotency of nil-algebra of nil-index n is equivalent to determining the smallest integer N such that the (n, N)-incidence matrix has rank equal to N!. In this work, we show that the (n, (equation omitted)$^{(1,....,n)}$-incidence matrix is center-symmetric.

• 충청수학회지
• /
• 제22권4호
• /
• pp.843-851
• /
• 2009

The purpose of this paper is to show that for each integer k where $1{\geq}k{\geq}2^{n-1}$, there exists an $n{\times}n(0,1)$-matrix A with exactly PerA = k. Thus we introduce a constructive approch for such matrices. Using the permanent of (0,1)-matrix, we decomposed the number n! with an linear combination of the power of 2. That coefficient is an stiring number.

• 대한수학회지
• /
• 제45권2호
• /
• pp.425-433
• /
• 2008

Let R be a ring with identity $1_R$ and let U(R) denote the group of all units of R. A ring R is called locally finite if every finite subset in it generates a finite semi group multiplicatively. In this paper, some results are obtained as follows: (1) for any semilocal (hence semiperfect) ring R, U(R) is a finite (resp. locally finite) group if and only if R is a finite (resp. locally finite) ring; U(R) is a locally finite group if and only if U$(M_n(R))$ is a locally finite group where $M_n(R)$ is the full matrix ring of $n{\times}n$ matrices over R for any positive integer n; in addition, if $2=1_R+1_R$ is a unit in R, then U(R) is an abelian group if and only if R is a commutative ring; (2) for any semiperfect ring R, if E(R), the set of all idempotents in R, is commuting, then $R/J\cong\oplus_{i=1}^mD_i$ where each $D_i$ is a division ring for some positive integer m and |E(R)|=$2^m$; in addition, if 2=$1_R+1_R$ is a unit in R, then every idempotent is central.

• 한국컴퓨터정보학회논문지
• /
• 제14권1호
• /
• pp.135-143
• /
• 2009

최근 모바일 장치에서 고해상도 영상의 인코딩 및 디코딩에 대한 요구가 늘어남에 따라 효율적인 영상 코덱 개발의 필요성이 증대되고 있다. 본 논문은 JPEG 디코딩 과정에서 IDCT 변환과 컬러변환 배열간의 선형성을 바탕으로 이들 연산순서를 재배열함으로써 컬러변환 과정에서 요구되는 계산 횟수를 줄이고 재배열된 부동소수점 연산에 정수 맵핑을 적용하여 시간 복잡도를 줄임으로써 실행시간을 크게 단축하는 컬러변환 기법을 제안한다. 또한, 제안된 기법은 연산 재배열 및 정수 맵핑의 양자화오류로 인한 화질 저하를 다중 모드 채도 재구성 기법을 적용하여 보상하도록 한다. 임베디드 시스템 개발 플랫폼에서의 성능평가를 통해 제안 된 기법이 기존의 컬러변환 기법들과 비교하여 복원 영상의 화질 저하를 최소화하면서 실행시간을 크게 단축함을 알 수 있었다.