• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.485-495
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• 2011

Let $A_1$ and $A_2$ be $n{\times}n$ nonzero complex matrices, denote a linear combination of the two matrices by $A=c_1A_1+c_2A_2$, where $c_1$, $c_2$ are nonzero complex numbers. In this paper, we research the problem of the linear combinations in the general case. We give a sufficient and necessary condition for A is an involutive matrix and s+1-potent matrix, respectively, where $A_1$ is a tripotent matrix, with $A_1A_2=A_2A_1$. Then, using the results, we also give the sufficient and necessary conditions for the involutory of the linear combination A, where $A_1$ is a tripotent matrix, anti-idempotent matrix, and involutive matrix, respectively, and $A_2$ is a tripotent matrix, idempotent matrix, and involutive matrix, respectively, with $A_1A_2=A_2A_1$.

• East Asian mathematical journal
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• 제40권3호
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• pp.329-339
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• 2024

In the work we generate arithmetic matrix P^(c,b,a) of (cx² + bx+a)ⁿ from a Pascal matrix P^(1,1). We extend an identity P^(1,1))O^(1,1) = P^(1,1,1) with an obtuse matrix O^(1,1) to k degree polynomials. For the purpose we study P^(1,1)kO^(1,1) and find generating polynomials of O^(1,1)k.

• East Asian mathematical journal
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• 제35권3호
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• pp.341-349
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• 2019

In this paper, we are concerned with the minimal positive solution to system of the nonlinear matrix equations $A_1X^2+B_1Y +C_1=0$ and $A_2Y^2+B_2X+C_2=0$, where $A_i$ is a positive matrix or a nonnegative irreducible matrix, $C_i$ is a nonnegative matrix and $-B_i$ is a nonsingular M-matrix for i = 1, 2. We apply Newton's method to system and present a modified Newton's iteration which is validated to be efficient in the numerical experiments. We prove that the sequences generated by the modified Newton's iteration converge to the minimal positive solution to system of nonlinear matrix equations.

• 대한수학회지
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• 제42권1호
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• pp.1-16
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• 2005

This paper presents a fast factorization algorithm for confluent Cauchy-like matrices. The algorithm consists of two parts. First. a confluent Cauchy-like matrix is transformed into a Cauchy-like matrix available to pivot without changing its structure. Second. a fast partial pivoting factorization algorithm for the Cauchy-like matrix is presented. A new displacement structure cannot possibly generate all entries of a transformed matrix, which is called by 'partially reconstructible'. This paper also discusses how the proposed factorization algorithm can be generally applied to partially reconstructive matrices.

• 대한수학회보
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• 제43권2호
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• pp.343-352
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• 2006

A real matrix A is called a sign-central matrix if for, every matrix $\tilde{A}$ with the same sign pattern as A, the convex hull of columns of $\tilde{A}$ contains the zero vector. A sign-central matrix A is called a tight sign-central matrix if the Hadamard (entrywise) product of any two columns of A contains a negative component. A real vector x = $(x_1,{\ldots},x_n)^T$ is called stable if $\|x_1\|{\leq}\|x_2\|{\leq}{\cdots}{\leq}\|x_n\|$. A tight sign-central matrix is called a $tight^*$ sign-central matrix if each of its columns is stable. In this paper, for a matrix B, we characterize those matrices C such that [B, C] is tight ($tight^*$) sign-central. We also construct the matrix C with smallest number of columns among all matrices C such that [B, C] is $tight^*$ sign-central.

• Kyungpook Mathematical Journal
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• 제19권1호
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• pp.127-134
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• 1979

A (0,1) matrix is acyclic if it does not have a permutation matrix of order 2 as a submatrix. A bipartite tournament is acyclic if and only if its adjacency matrix is acyclic. The concepts of (maximal) order of cyclicity of a matrix and a bipartite tournament are introduced and studied.

• 한국통신학회논문지
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• 제27권2A호
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• pp.116-123
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• 2002

자켓 행렬(Jacket matrix)은 왈쉬 하다마드(Walsh Hadamard) 행렬 구조를 바탕으로 확장한 행렬이다. 왈쉬 하다마드 행렬이 +1, -1을 기본 원소로 하고 있는 반면 자켓 행렬은 $\pm$1과 $\pm$$\omega$($\pm$j, $\pm$$_2$$^{n}$ )를 각각 원소로 가질 수 있다. 이 행렬은 중앙 부근에 무게(weight)를 갖는데, 하다마드 행렬 크기의 1/4 크기로 부호 부분과 무게 부분으로 구성된다. 본 논문에서는 기존에 행렬 중앙에 강제적으로 무게를 할당하여 자켓 행렬을 구성하였으나, 어떠한 크기의 행렬도 크기와 무게만 정해주면 생성해낼 수 있는 이진 인덱스를 이용한 간단한 비트열 형태의 일반식이 제시된다. 무게는 행과 열의 이진 인덱스의 최상위 두 비트를 Exclusive-OR 연산한 결과가 1인 원소에 부여된다. 또한 분산연산(Distributed Arithmetic:DA) 알고리즘을 이용한 고속자켓변환(Fast Jacket Transform)의 VLSI 구조를 제시한다. 자켓 행렬은 cyclic한 특성을 가지고 있어서 암호화, 정보 이론 및 WCDMA의 복소수 확산 QPSK 변조부에 응용될 수 있다.

• 한국동물학회지
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• 제37권3호
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• pp.318-323
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• 1994

The association of replication origins/termini with nuclear matrix during S phase was investigated by DNase digestion of halo structures in synchronized mouse LPI-1 cells. The binding of parental DNA to nuclear matrix was constant throughout S phase. When nuclear matrix was isolated from the cells pulse-labeled with 3H-thvmidine at various stases of S phase, total 3H-labels associated with nuclear matrix were specifically higher at So, Sa and Ss stages than other stases of S phase, suggesting that the newly synthesized DNAs at those stages are not excluded out of nuclear matrix. Similar patterns were obsenred from the pulse-chase experiments, in which cells were pulse-labeled at each stage of S phase and further incubated for 1 hr. These results suggest that the replication origins and termini are fixed at the nuclear matrix, and that the nuclear matrix binding fractions of DNA at 3C-pause may contain a large population of replication origins and termination sites.

• 호남수학학술지
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• 제41권1호
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• pp.35-49
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• 2019

In this work, it is shown that the combination of operational techniques and the use of the principle of quasi-monomiality can be a very useful tool for a more general insight into the theory of matrix polynomials and for their extension. We explore the formal properties of the operational rules to derive a number of properties of certain class of matrix polynomials and discuss the operational links with various known matrix polynomials.

• 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.