• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.765-771
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• 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.

• Kyungpook Mathematical Journal
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• v.43 no.4
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• pp.605-616
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• 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.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.227-237
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• 2014

For an $m{\times}n$ nonnegative integral matrix A, a generalized inverse of A is an $n{\times}m$ nonnegative integral matrix G satisfying AGA = A. In this paper, we characterize nonnegative integral matrices having generalized inverses using the structure of nonnegative integral idempotent matrices. We also define a space decomposition of a nonnegative integral matrix, and prove that a nonnegative integral matrix has a generalized inverse if and only if it has a space decomposition. Using this decomposition, we characterize nonnegative integral matrices having reflexive generalized inverses. And we obtain conditions to have various types of generalized inverses.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.247-260
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• 2015

The special form of Schur complement is extended to have a Schur's formula to obtains the explicit formula of determinant, inverse, and eigenvector formula of the doubly Leslie matrix which is the generalized forms of the Leslie matrix. It is also a generalized form of the doubly companion matrix, and the companion matrix, respectively. The doubly Leslie matrix is a nonderogatory matrix.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.407-413
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• 2007

In this paper, we definite a generalized weighted Moore-Penrose inverse $A^{+}_{M,N}$ of a given matrix A, and give the necessary and sufficient conditions for its existence. We also prove its uniqueness and give a representation of it. In the end we point out this generalized inverse is also a prescribed rang T and null space S of {2}-(or outer) inverse of A.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.415-424
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• 2007

The generalized inverses have many important applications in the aspects of theoretic research and numerical computations and therefore they were studied by many authors. In this paper we get some necessary and sufficient conditions of the forward order law for {1}-inverse of multiple matrices products $A\;=\;A_1A_2{\cdots}A_n$ by using the maximal rank of generalized Schur complement.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.487-498
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• 2007

In this paper, we obtain important combinatorial identities of generalized harmonic numbers using symmetric polynomials. We also obtain the matrix representation for the generalized harmonic numbers whose inverse matrix can be computed recursively.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.8
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• pp.147-159
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• 1994

The performance of the improvement method of spatial resolution for satellite images based on the generalized inverse matrix is superior to the conventional methods. But, this method calculates the coefficient values for extracting the spatial information from the relation between a small pixel and large pixels. Accordingly it has the problem of remaining the blocky patterns at the result image. In this paper, a new generalized inverse matrix method is proposed which is different in the calculation method of coefficient values for extracting the spatial information. In this proposed metod, it calculates the coefficient values for extracting the spatial information from the relation between a small pixel and small pixels. Consequently it can improve the spatial resolution more efficiently without remaining the blocky patterns at the result image. The effectiveness of the proposed method is varified by simulation experiments with real TM image data.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.81-94
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• 2007

In this paper we investigate symbolic implementation of two modifications of the Leverrier-Faddeev algorithm, which are applicable in computation of the Moore-Penrose and the Drazin inverse of rational matrices. We introduce an algorithm for computation of the Drazin inverse of rational matrices. This algorithm represents an extension of the papers [11] and [14]. and a continuation of the papers [15, 16]. The symbolic implementation of these algorithms in the package MATHEMATICA is developed. A few matrix equations are solved by means of the Drazin inverse and the Moore-Penrose inverse of rational matrices.

• Journal of Mechanical Science and Technology
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• v.16 no.8
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• pp.1072-1078
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• 2002

The constrained motion requires the determination of constraint force acting on unconstrained systems for satisfying given constraints. Most of the methods to decide the force depend on numerical approaches such that the Lagrange multiplier method, and the other methods need vector analysis or complicated intermediate process. In 1992, Udwadia and Kalaba presented the generalized inverse method to describe the constrained motion as well as to calculate the constraint force. The generalized inverse method has the advantages which do not require any linearization process for the control of nonlinear systems and can explicitly describe the motion of holonomically and/or nongolonomically constrained systems. In this paper, an explicit equation to describe the constrained motion is derived by minimizing the performance index, which is a function of constraint force vector, with respect to the constraint force. At this time, it is shown that the positive-definite weighting matrix in the performance index must be the inverse of mass matrix on the basis of the Gauss's principle and the derived differential equation coincides with the generalized inverse method. The effectiveness of this method is illustrated by means of two numerical applications.