• Honam Mathematical Journal
• /
• v.30 no.2
• /
• pp.399-409
• /
• 2008

We consider the most generalized quadratic matrix equation, Q(X) = $A_7XA_6XA_5+A_4XA_3+A_2XA_1+A_0=0$, where X is m ${\times}$ n, $A_7$, $A_4$ and $A_2$ are p ${\times}$ m, $A_6$ is n ${\times}$ m, $A_5$, $A_3$ and $A_l$ are n ${\times}$ q and $A_0$ is p ${\times}$ q matrices with complex elements. The convergence of Newton's method for solving some different types of quadratic matrix equations are considered and we show that the elementwise minimal positive solvents can be found by Newton's method with the zero starting matrices. We finally give numerical results.

• Information Systems Review
• /
• v.2 no.2
• /
• pp.193-199
• /
• 2000

• The Journal of the Korea institute of electronic communication sciences
• /
• v.12 no.1
• /
• pp.101-108
• /
• 2017

As the quantum gate matrix is a $r^{n+1}{\times}r^{n+1}$ dimension when the radix is r, the number of control state vectors is n, and the number of target state vectors is one, the matrix dimension with increasing n is exponentially increasing. If the number of control state vectors is $2^n$, then the number of $2^n-1$ unit matrix operations preserves the output from the input, and only one can be performed the unitary operation to the target state vector. Therefore, this paper proposes a new method of function embedding that can replace $2^n-1$ times of unit matrix operations with deterministic contribution to matrix dimension by arithmetic power switch of the unitary gate. The proposed function embedding method uses a binary literal switch with a multivalued threshold, so that a general purpose hybrid MCU gate can be realized in a $r{\times}r$ unitary matrix.

• The Korean Journal of Nuclear Medicine Technology
• /
• v.14 no.1
• /
• pp.94-100
• /
• 2010

Purpose: We can evaluate function of kidney by Glomerular Filtration Rate (GFR) test using $^{99m}Tc$-DTPA which is simple. This test is influenced by several parameter such as net syringe count, kidney depth, corrected kidney count, acquisition time and characters of gamma camera. In this study, we evaluated predose count according to matrix size in the GFR test using $^{99m}Tc$-DTPA. Materials and Methods: Gamma camera of Infinia in GE was used, and LEGP collimator, three types of matrix size ($64{\times}64$, $128{\times}128$, $256{\times}256$) and 1.0 of zoom factor were applied. We increased radioactivity concentration from 222 (6), 296 (8), 370 (10), 444 (12) up to 518 MBq (14 mCi) respectively and acquired images according to matrix size at 30 cm distance from detector. Lastly, we evaluated these values and then substituted them for GFR formula. Results: In $64{\times}64$, $128{\times}128$ and $256{\times}256$ of matrix size, counts per second was 26.8, 34.5, 41.5, 49.1 and 55.3 kcps, 25.3, 33.4, 41.0, 48.4 and 54.3 kcps and 25.5, 33.7, 40.8, 48.1 and 54.7 kcps respectively. Total counts for 5 second were 134, 172, 208, 245 and 276 kcounts from $64{\times}64$, 127, 172, 205, 242, 271 kcounts from $128{\times}128$, and 137, 168, 204, 240 and 273 kcounts from $256{\times}256$, and total counts for 60 seconds were 1,503, 1,866, 2,093, 2,280, 2,321 kcounts, 1,511, 1,994, 2,453, 2,890 and 3,244 kcounts, and 1,524, 2,011, 2,439, 2,869 and 3,268 kcounts respectively. It is different from 0 to 30.02 % of percentage difference in $64{\times}64$ of matrix size. But in $128{\times}128$ and $256{\times}256$, it is showed 0.60 and 0.69 % of maximum value each. GFR of percentage difference in $64{\times}64$ represented 6.77% of 222 MBq (6 mCi), 42.89 % of 518 MBq (14 mCi) at 60 seconds respectively. However it is represented 0.60 and 0.63 % each in $128{\times}128$ and $256{\times}256$. Conclusion: There was no big difference in total counts of percentage difference and GFR values acquiring from $128{\times}128$ and $256{\times}256$ of matrix size. But in $64{\times}64$ of matrix size when the total count exceeded 1,500 kcounts, the overflow phenomenon was appeared differently according to predose radioactivity of concentration and acquisition time. Therefore, we must optimize matrix size and net syringe count considering the total count of predose to get accurate GFR results.

• 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.

• The Transactions of the Korean Institute of Electrical Engineers P
• /
• v.63 no.3
• /
• pp.200-205
• /
• 2014

In this paper, 5.8GHz band $4{\times}4$ Butler matrix is designed using easily accessible commercial $90^{\circ}$ hybrid coupler and semirigid coaxial cable as a transmission line. This Butler matrix is very flexible to changes of antenna system specification like a frequency band because $90^{\circ}$ hybrid coupler changing is all to do. The result of design is the distance of $2{\times}2$ array antenna element is $\sqrt{2}{\lambda}/4$, the 4 beam directions are diagonal of array antenna and phase shifter is not necessary. The beam width is roughly $25^{\circ}$ narrower because of array antenna geometry and the side lobe is about 10dB higher partially than theoretical beam pattern. But the overall beam pattern is similar with theoretical beam. This Butler matrix can be applied to switching beam antenna of 5.8GHz band Wi-Fi and WAVE system.

• Communications of the Korean Mathematical Society
• /
• v.12 no.2
• /
• pp.269-273
• /
• 1997

We show that each element in the semigroup $S_n$ of all $n \times n$ non-singular stochastic totally positive matrices is generated by the infinitesimal elements of $S_n$, which form a cone consisting of all $n \times n$ Jacobi intensity matrices.

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

• Honam Mathematical Journal
• /
• v.21 no.1
• /
• pp.57-64
• /
• 1999

Let K be a algebraically closed field of characteristic 0 and G be abelian group $Z_2{\times}Z_2{\times}Z_2$ or $Z_2{\times}Z_4$. We find the conditions which the elements of the group ring KG are unit and idempotent respecting using the basic table matrix of G. We can see that if ${\alpha}={\sum}r(g)g$ is an idempotent element of KG, then $r(1)=0,\;\frac{1}{{\mid}G{\mid}},\;\frac{2}{{\mid}G{\mid}},\;{\cdots},\frac{{\mid}G{\mid}-1}{{\mid}G{\mid}},\;1$.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.15 no.5
• /
• pp.39-49
• /
• 2015

Some characters and construction theorems of Pseudo Jacket Matrix which is generalized from Jacket Matrix introduced by Jacket Matrices: Construction and Its Application for Fast Cooperative Wireless signal Processing[27] was announced. In this paper, we proposed some examples of Pseudo inverse Jacket matrix, such as $2{\times}4$, $3{\times}6$ non-square matrix for the MIMO channel. Furthermore we derived MIMO singular value decomposition (SVD) pseudo inverse channel and developed application to utilize SVD based on channel estimation of partitioned antenna arrays. This can be also used in MIMO channel and eigen value decomposition (EVD).