• Journal of applied mathematics & informatics
• /
• 제18권1_2호
• /
• pp.45-57
• /
• 2005

An efficient algorithm for finding the inverse and the group inverse of the FLS $\gamma-circulant$ matrix is presented by Euclidean algorithm. Extension is made to compute the inverse of the FLS $\gamma-retrocirculant$ matrix by using the relationship between an FLS $\gamma-circulant$ matrix and an FLS $\gamma-retrocirculant$ matrix. Finally, some examples are given.

• 대한수학회보
• /
• 제51권3호
• /
• pp.765-771
• /
• 2014

Necessary and sufficient conditions for the existence of the group inverse of an anti-triangular block matrix in Banach algebras are presented. Using these results, we give the formulae for the generalized Drazin inverse of a block matrix.

• Journal of applied mathematics & informatics
• /
• 제17권1_2_3호
• /
• 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.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 2007년도 심포지엄 논문집 정보 및 제어부문
• /
• pp.281-282
• /
• 2007

We address a new representation of DCT/DFT/Wavelet matrices via one hybrid architecture. Based on an element inverse matrix factorization algorithm, we show that the OCT, OFT and Wavelet which based on Haar matrix have the similarrecursive computational pattern, all of them can be decomposed to one orthogonal character matrix and a special sparse matrix. The special sparse matrix belongs to Jacket matrix, whose inverse can be from element-wise inverse or block-wise inverse. Based on this trait, we can develop a hybrid architecture.

• Journal of electromagnetic engineering and science
• /
• 제6권4호
• /
• pp.244-252
• /
• 2006

A block Jacket transform and. its block inverse Jacket transformn have recently been reported in the paper 'Fast block inverse Jacket transform'. But the multiplication of the block Jacket transform and the corresponding block inverse Jacket transform is not equal to the identity transform, which does not conform to the mathematical rule. In this paper, new binary block Jacket transforms and the corresponding binary block inverse Jacket transforms of orders $N=2^k,\;3^k\;and\;5^k$ for integer values k are proposed and the mathematical proofs are also presented. With the aid of the Kronecker product of the lower order Jacket matrix and the identity matrix, the fast algorithms for realizing these transforms are obtained. Due to the simple inverse, fast algorithm and prime based $P^k$ order of proposed binary block inverse Jacket transform, it can be applied in communications such as space time block code design, signal processing, LDPC coding and information theory. Application of circular permutation matrix(CPM) binary low density quasi block Jacket matrix is also introduced in this paper which is useful in coding theory.

• 한국통신학회논문지
• /
• 제32권4C호
• /
• pp.440-446
• /
• 2007

본 논문은 엘레멘트 인버스 처리에 근거한 재킷 변환을 통한 DFT 행렬의 새로운 표현을 다룬다. DFT 행렬의 역을 단지 재킷 변환의 소행렬 분해에 따라 표현하며 이러한 결과는 DFT 행렬의 역이 단지 이의 희소 행렬과 치환 행렬에만 관련됨을 보여준다. 재킷 행렬을 통한 DFT 행렬의 분해는 블록 변조 특성을 나타내는 강한 기하 구조를 갖는다. 이는 재킷 행렬을 통해 분해된 DFT 행렬은 블록 변조 과정으로 해석할 수 있음을 의미한다.

• Kyungpook Mathematical Journal
• /
• 제43권4호
• /
• pp.605-616
• /
• 2003

In this paper, some rank equalities related to generalized inverses $A^{(2)}_{T,S}$ of a matrix are presented. As applications, a variety of rank equalities related to the M-P inverse, the Drazin inverse, the group inverse, the weighted M-P inverse, the Bott-Duffin inverse and the generalized Bott-Duffin inverse are established.

• Journal of the Korean Data and Information Science Society
• /
• 제14권4호
• /
• pp.1007-1012
• /
• 2003

A recursive procedure for finding the Cholesky root of the inverse of sample covariance matrix, leading to a direct solution for the inverse of a positive definite matrix, is developed using the likelihood equation for the maximum likelihood estimation of the Cholesky root under normality assumptions. An example of the Hilbert matrix is considered for an illustration of the procedure.

• 한국공간구조학회논문집
• /
• 제2권1호
• /
• pp.75-84
• /
• 2002

In this study, the 'force density method' for shape finding of cable net structures is presented. This concept is based on the force-length ratios or force densities which are defined for each branch of the net structures. This method renders a simple linear 'analytical form finding' possible. If the free choice of the force densities is restricted by further condition, the linear method is extended to a nonlinear one. The nonlinear one can be applied to the detailed computation of networks. In this paper, the general inverse matrix is introduced to solve the nonlinear equilibrium equation including Jacobian matrix which is rectangular matrix. Several examples for linear and nonlinear analysis applied additional constraints are presented. It is shown that the force density method is suitable for form finding of cable net and the general inverse matrix can be applied to solve the nonlinear equation without Lagrangian factors.

• 제어로봇시스템학회논문지
• /
• 제22권7호
• /
• pp.519-523
• /
• 2016

This paper proposes a method of estimating the actuator faults of a hexacopter without using encoders when one or more of six actuators do not operate normally. In the case of the hexacopter, a Pseudo-Inverse matrix is generally used to obtain the rotational speed of the actuators because the matrix that transforms the rotational speed of the actuators into the thrust and torque of the body coordinate system is not a square matrix. However, the method based on the Pseudo-Inverse matrix cannot detect the actuator faults correctly because the Pseudo-Inverse matrix is approximate. In the proposed method, the actuator faults are estimated by modifying the transform matrix using the property that the actuators of the hexacopter are symmetrical. The simulation results show the effectiveness of the proposed method when faults occur in one or more of the six actuators.