• 호남수학학술지
• /
• 제19권1호
• /
• pp.157-164
• /
• 1997

We are concerned with three classes of matrices that are relevant to the linear complementary problem. We prove that within the class of $P_0$-matrices, the Q-matrices are precisely the regular matrices and we show that the same characterizations hold for an L-matrix as well, and that the symmetric copositive-plus Q-matrices are precisely those which are strictly copositive.

• Kyungpook Mathematical Journal
• /
• 제59권3호
• /
• pp.505-513
• /
• 2019

In this paper, we study orthanogonal polynomials by looking at their comrade matrices and reachability matrices. First, we focus on the algebraic structure that is exhibited by comrade matrices. Then, we explain some properties of this algebraic structure which helps us to find a connection between comrade matrices and reachability matrices. In the last section, we use this connection to determine the determinant, eigenvalues, and eigenvectors of these matrices. Finally, we derive a factorization for det R(A, x), where R(A, x) is the reachability matrix for a comrade matrix A and x is a vector of indeterminates.

• Korean Journal of Mathematics
• /
• 제9권1호
• /
• pp.53-60
• /
• 2001

We study the properties of positivity of matrices and construct useful positive matrices. As an application, we consider a directed graph with matrices such that all the associated matrices related to the positive linear functional are positive.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제14권6호
• /
• pp.2497-2517
• /
• 2020

For compressed sensing (CS) applications, it is significant to construct deterministic measurement matrices with good practical features, including good sensing performance, low memory cost, low computational complexity and easy hardware implementation. In this paper, a deterministic construction method of bipolar measurement matrices is presented based on binary sequence family (BSF). This method is of interest to be applied for sparse signal restore and image block CS. Coherence is an important tool to describe and compare the performance of various sensing matrices. Lower coherence implies higher reconstruction accuracy. The coherence of proposed measurement matrices is analyzed and derived to be smaller than the corresponding Gaussian and Bernoulli random matrices. Simulation experiments show that the proposed matrices outperform the corresponding Gaussian, Bernoulli, binary and chaotic bipolar matrices in reconstruction accuracy. Meanwhile, the proposed matrices can reduce the reconstruction time compared with their Gaussian counterpart. Moreover, the proposed matrices are very efficient for sensing performance, memory, complexity and hardware realization, which is beneficial to practical CS.

• 대한수학회지
• /
• 제48권1호
• /
• pp.83-104
• /
• 2011

In this note, compound-commuting additive maps on matrix spaces are studied. We show that compound-commuting additive maps send rank one matrices to matrices of rank less than or equal to one. By using the structural results of rank-one nonincreasing additive maps, we characterize compound-commuting additive maps on four types of matrices: triangular matrices, square matrices, symmetric matrices and Hermitian matrices.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제7권2호
• /
• pp.51-64
• /
• 2003

Analysis is given of construction and stability of complex symmetric analogues of Householder matrices, with applications to the eigenproblem for such matrices. We investigate numerical properties of the deflation of complex symmetric matrices by using complex symmetric Householder transformations. The proposed method is very similar to the well-known deflation technique for real symmetric matrices (Cf. [16], pp. 586-595). In this paper we present an error analysis of one step of the deflation of complex symmetric matrices.

• 대한수학회보
• /
• 제58권3호
• /
• pp.609-616
• /
• 2021

We study the solvability of the Fermat's matrix equation in some classes of 2-by-2 matrices. We prove the Fermat's matrix equation has infinitely many solutions in a set of 2-by-2 positive semidefinite integral matrices, and has no nontrivial solutions in some classes including 2-by-2 symmetric rational matrices and stochastic quadratic field matrices.

• Journal of applied mathematics & informatics
• /
• 제29권5_6호
• /
• pp.1571-1581
• /
• 2011

In this paper, we construct inequivalent Hadamard matrices based on several new and old full orthogonal designs, using circulant and symmetric block matrices. Not all orthogonal designs produce inequivalent Hadamard matrices, because the corresponding systems of equations do not possess solutions. The systems of equations arising when we search for inequivalent Hadamard matrices from full orthogonal designs using circulant and symmetric block matrices, can be concisely described using the periodic autocorrelation function of the generators of the block matrices. We use Maple, Magma, C and Unix tools to find many new inequivalent Hadamard matrices.

• 한국자기공명학회논문지
• /
• 제4권2호
• /
• pp.91-102
• /
• 2000

The photoproduced cation radical of N-methylphenothiazine doped in the different kind of matrices of phenyltriethoxysilane (PhiTEOS), vinyltriethoxysilane (VTEOS), and methyloiethoxysilane (METOS) was comparatively studied with electron spin resonance (ESR) and electron nuclear double resonance (ENDOR). The photoinduced charge separation efficiency was determined by integration of ESR spectra which correspond to the amount of photoproduced cation radical in the matrices. This was correlatively studied with the polarity and pore size of the gel matrices. The polarity of the matrices was comparatively determined by measuring λ$\sub$max/ values of PC$_1$ in the different matrices. The relative pore size among the matrices was determined by measuring relative proton matrix ENDOR line widths of the photoproduced cation radical of PCI. The decay kinetic constants of the cation radical of PCI in the different matrices was relatively studied with fitting the biexponential decay curves after exposure into the ambient condition. This is correlatively interpreted with the polarity and pore size of the matrices.

• 대한수학회논문집
• /
• 제16권4호
• /
• pp.679-690
• /
• 2001

Doubly stochastic matrices are n$\times$n nonnegative ma-trices whose row and column sums are all 1. Convex polytope $\Omega$$_{n}$ of doubly stochastic matrices and more generally (R,S), so called transportation polytopes, are important since they form the domains for the transportation problems. A theorem by Birkhoff classifies the extremal matrices of , $\Omega$$_{n}$ and extremal matrices of transporta-tion polytopes (R,S) were all classified combinatorially. In this article, we consider signed version of $\Omega$$_{n}$ and (R.S), obtain signed Birkhoff theorem; we define a new class of convex polytopes (R,S), calculate their dimensions, and classify their extremal matrices, Moreover, we suggest an algorithm to express a matrix in (R,S) as a convex combination of txtremal matrices. We also give an example that a polytope of signed matrices is used as a domain for a decision problem. In this context of finite reflection(Coxeter) group theory, our generalization may also be considered as a generalization from type $A_{*}$ n/ to type B$_{n}$ D$_{n}$. n/.