• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.3
• /
• pp.589-599
• /
• 2012

An element of a ring is called strongly nil clean provided that it can be written as the sum of an idempotent and a nilpotent element that commute. We characterize, in this article, the strongly nil cleanness of $2{\times}2$ and $3{\times}3$ matrices over $R[x]/(x^2-1)$ where $R$ is a commutative local ring with characteristic 2. Matrix decompositions over fields are derived as special cases.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.3 no.1
• /
• pp.43-53
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.3
• /
• pp.511-519
• /
• 2009

A matrix $P{\in}\mathbb{C}^{n{\times}n}$ is called a generalized reflection matrix if $P^*$ = P and $P^2$ = I. An $n{\times}n$ complex matrix A is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix P if A = PAP (A = -PAP). It is well-known that the reflexive and anti-reflexive matrices with respect to the generalized reflection matrix P have many special properties and widely used in engineering and scientific computations. In this paper, we give new necessary and sufficient conditions for the existence of the reflexive (anti-reflexive) solutions to the linear matrix equation AXB + CY D = E and derive representation of the general reflexive (anti-reflexive) solutions to this matrix equation. By using the obtained results, we investigate the reflexive (anti-reflexive) solutions of some special cases of this matrix equation.

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.4
• /
• pp.759-767
• /
• 2011

An element of a ring is called strongly nil clean provided that it can be written as the sum of an idempotent and a nilpotent element that commute. A ring is strongly nil clean in case each of its elements is strongly nil clean. We investigate, in this article, the strongly nil cleanness of 2${\times}$2 matrices over local rings. For commutative local rings, we characterize strongly nil cleanness in terms of solvability of quadratic equations. The strongly nil cleanness of a single triangular matrix is studied as well.

• Proceedings of the IEEK Conference
• /
• 2002.06b
• /
• pp.257-260
• /
• 2002

This paper describes the pixel of AMOLED(act ive matrix organic light emitting diode) driving circuit by poly-sl technology. The area per pixel is 278um$\times$278um in 120$\times$160(2.2 inch) Driving the OLEDS with active matrix leads to the lower voltage operation, the lower peak pixel currents and the display with much greater efficiency and brightness The role of the active matrix is to provide a constant current throughout the entire frame time and is eliminating the high currents encountered In the passive matrix approach, This design can support the high resolutions expected by the consumer because the current variation specification is norestricted. The pixel has been designed driving TFT threshold voltage cancellation circuit and wide aperture ratio circuit that communizes 4 pixel. The test simulation results and layout are 11% per threshold-current var Eat ion and 12.5% the aperture ratio of increase.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
• /
• v.26 no.10
• /
• pp.876-884
• /
• 2015

In this paper, a switched beamforming antenna system at 28 GHz frequency band is described for $5^{th}$ generation wireless communication. The butler matrix is used as a beamforming system and it produces linear spaced phase difference at four output ports. Array antenna is designed that can be steered in desired 4 different directions 28 GHz frequency band. Operation of designed butler matrix that composed of couplers and feedline is explained. The antenna system is designed in RO3003 substrate that has a height of 5 mil and dielectric constant of 3. The size of butler matrix is $20.3{\times}13.0mm^2$ and size of array antenna is $21.2{\times}19.9mm^2$. This system can be steered from $-34^{\circ}$ to $33^{\circ}$ and minimum sidelobe level is 12.9 dB.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.25 no.10A
• /
• 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.

• East Asian mathematical journal
• /
• v.29 no.3
• /
• pp.327-335
• /
• 2013

In this paper we consider the quadratic matrix equation which can be defined by $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown complex matrix, and A, B and C are $n{\times}n$ given matrices with complex elements. We first introduce a couple of condition numbers of the equation Q(X) and present normwise condition numbers. Finally, we compare the results and some numerical experiments are given.

• The Korean Journal of Applied Statistics
• /
• v.26 no.6
• /
• pp.999-1007
• /
• 2013

This research shows several types of moving pictures from the data: 1) the word cloud of Korean texts, 2) the heat map of n ${\times}$ p matrices, 3) the moving image of p ${\times}$ p scatterplot matrix, 4) the local projective display of k clusters (Huh and Lee, 2012). Moving pictures may reveal the hidden information and beauty of the datasets and ignite the curiosity of information consumers. Video files are attached.