• Journal of applied mathematics & informatics
• /
• v.17 no.1_2_3
• /
• pp.585-590
• /
• 2005

An efficient procedure for finding the inverse of a nonsingular matrix is developed by solving directly for the UL decomposition of the inverse based on the entries of the original nonsingular matrix.

• Journal of applied mathematics & informatics
• /
• v.20 no.1_2
• /
• pp.421-431
• /
• 2006

In this paper, we establish a matrix inequality and its equivalent form. Applying the results, some matrix inequalities involving Khatri-Rao products of positive semi-definite matrices are generalized.

• Journal of the Korean Mathematical Society
• /
• v.50 no.4
• /
• pp.755-770
• /
• 2013

One of the interesting nonlinear matrix equations is the quadratic matrix equation defined by $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown real matrix, and A, B and C are $n{\times}n$ given matrices with real elements. Another one is the matrix polynomial $$P(X)=A_0X^m+A_1X^{m-1}+{\cdots}+A_m=0,\;X,\;A_i{\in}\mathbb{R}^{n{\times}n}$$. Newton's method is used to find the symmetric and bisymmetric solvents of the nonlinear matrix equations Q(X) and P(X). The method does not depend on the singularity of the Fr$\acute{e}$chet derivative. Finally, we give some numerical examples.

• Journal of applied mathematics & informatics
• /
• v.25 no.1_2
• /
• pp.505-511
• /
• 2007

Recently, the equivalent relations between a symmetric dual problem and a matrix game B(x, y) were given in [6: D.S. Kim and K. Noh, J. Math. Anal. Appl. 298(2004), 1-13]. Using more simpler form of B(x, y) than one in [6], we establish the equivalence relations between a symmetric dual problem and a matrix game, and then give a numerical example illustrating our equivalence results.

• Communications for Statistical Applications and Methods
• /
• v.7 no.1
• /
• pp.285-290
• /
• 2000

We noted a property of a stationary distribution on the matrix C, which is the covariance matrix of order statistics of standard normal distribution That is the sup norm of th powers of C is ee' divided by its dimension. The matrix C can be taken as a transition probability matrix in an acyclic Markov chain.

• Journal of Radiation Protection and Research
• /
• v.11 no.1
• /
• pp.3-14
• /
• 1986

A stud has been carried out for figuring out real photon spectrum from an observed gamma-ray spectrum by means of response matrix method, which is known one of the relatively convenient method for the estimation of exposure rate of a complex gamma ray field in comparison with graphical analysis and least square fitting of the measured spectrum. A 3'${\times}$3' cylindrical Nal(T1) scintillation detector in association with multichannel pulse height analyzer and six reference gamma ray sources covering the photon energy range of 0.05 to 2.0 MeV were used. In dividing the energy region for the construction of response matrix, two different approaches were attempted. One is dividing the entire energy region of interest into 20 bins, one of which corresponds to a width of 0.1 MeV to form $20{\times}20$ matrix, and another is dividing the 2 MeV region into 14 bins to form $14{\times}14$ matrix consists of $0.1(MeV)^{1/2}$ intervals assuming the resolution of the detector is dependent on square root of the incident photon energy. Inversion of thus constructed matrices was performed by a computor(P-E8/32) using the program attached to the end of this paper. The resultant exposure rates obtained by this method were in good agreement, within 10% with those calculated by ordinary formula widely used for a gamma-ray field of known energy and flux. It is concluded that the photen flux obtained by the response matrix constructed under the assumption of $E^{1/2}$ dependence is more realistic than that obtained by the matrix consist of identical energy bins in dosimetrical point of view.

• Communications for Statistical Applications and Methods
• /
• v.12 no.3
• /
• pp.653-657
• /
• 2005

Eigenstructure of a spatial design matrix of Matheron's variogram estimator in $R^1$ is derived. It is shown that the spatial design matrix in $R^1$ with n/2$\le$h < n has a nice spectral decomposition. The mean, variance, and covariance of this estimator are obtained using the eigenvalues of a spatial design matrix. We also found that the lower bound and the upper bound of the normalized Matheron's variogram estimator.

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.1
• /
• pp.1-7
• /
• 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 $U{\in}GL_n(R)$.

• Mass Spectrometry Letters
• /
• v.4 no.1
• /
• pp.21-23
• /
• 2013

The effects of trifluoroacetic acid (TFA) were evaluated on the generation of multiply charged ions of cytochrome c in a 2-nitrophloroglucinol (2-NPG) matrix in high-vacuum, matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS). The presence of 1% TFA in the 2-NPG matrix solution was more effective in generating multiply charged protein ions than matrix solutions containing 0.1% or 0% TFA. Regarding the matrix itself, with 1% TFA, 2-NPG was significantly more effective in generating multiply charged ions than 2,5-dihydroxybenzoic acid (2,5-DHB). The maximum charge state of cytochrome c was +8 when using a 2-NPG matrix containing 1% TFA.

• Journal of the Korean Statistical Society
• /
• v.13 no.2
• /
• pp.114-120
• /
• 1984

A parallel flats fraction for the $3^n$ design is defined as union of flats ${t}At=c_i(mod 3)}, i=1,2,\cdots, f$ and is symbolically written as At=C where A is rank r. The A matrix partitions the effects into n+1 alias sets where $u=(3^{n-r}-1)/2. For each alias set the f flats produce an ACPM from which a detection matrix is constructed. The set of all possible parallel flats fraction C can be partitioned into equivalence classes. In this paper, we develop some properties of a detection matrix and C.