• East Asian mathematical journal
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• v.29 no.3
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• pp.259-268
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• 2013

There are a lot of unsolved problems or issues regarding Kronecker products, vec-operator and Commutation matrices. We derived further properties and results of Kronecker products, vec-operator and Commutation Matrices.

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.651-658
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• 2001

The projection matrix plays an important role in the linear model theory. In this paper we derive an algebraic relationship between the projection matrices of submatrices of the design matrix. Using this relationship we can easily obtain the projection matrices of any submatrices of the design matrix. Also we show that every projection matrix can be obtained as a linear combination of Kronecker products of identity matrices and matrices with all elements equal to 1.

• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.1
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• pp.173-176
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• 1987

This paper presents a simple factorization of the Hadamard matrix which is used to develop a fast algorithm for the Hadamard transform. This matrix decomposition is of the kronecker products of identity matrices and successively lower order Hadamard matrices. This following shows how the Kronecker product can be mathematically defined and efficiently implemented using a factorization matrix methods.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.101-109
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• 2002

We extend two inequalities involving Hadamard Products of Positive definite Hermitian matrices to positive semi-definite Hermitian matrices. Simultaneously, we also show the sufficient conditions for equalities to hold. Moreover, some other matrix inequalities are also obtained. Our results and methods we different from those which are obtained by S. Liu in [J. Math. Anal. Appl. 243:458-463(2000)] and B.-Y Wang et al in [Lin. Alg. Appl. 302-303: 163-172(1999)] .

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.125-133
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• 2002

Recently, Several inequalities Khatri-Rao Products of two four partitioned blocks positive definite real symmetry matrices are established by Liu in[Lin. Alg. Appl. 289(1999): 267-277]. We extend these results in two ways. First, the results are extended to two any partitioned blocks Hermitian matrices. Second, necessary and sufficient conditions under which these inequalities become equalities are presented.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.99-112
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• 2020

The study is about the bounds of the spectral norms of r-circulant and geometric circulant matrices with the sequences called biperiodic Jacobsthal numbers. Then we give bounds for the spectral norms of Kronecker and Hadamard products of these r-circulant matrices and geometric circulant matrices. The eigenvalues and determinant of r-circulant matrices with the bi-periodic Jacobsthal numbers are obtained.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.39 no.6
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• pp.598-606
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• 1990

Common problems encountered when orthogonal functions are used in system analysis and state estimation are the time consuming process of high order matrix inversion required in finding the Kronecker products and the truncation errors. In this paper, therefore, a method for the analysis of bilinear systems using Walsh, Block pulse, and Haar functions is devised, Then, state estimation of bilinear system is also studied based on single term expansion of orthogonal functions. From the method presented here, when compared to the other conventional methods, we can obtain the results with simpler computation as the number of interval increases, and the results approach the original function faster even at randomly chosen points regardless of the definition of intervals. In addition, this method requires neither the inversion of large matrices on obtaining the expansion coefficients nor the cumbersome procedures in finding Kronecker products. Thus, both the computing time and required memory size can be significantly reduced.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.16 no.1
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• pp.85-91
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• 2002

Generally when the orthogonal functions are used in system analysis, the time consuming processes of high order matrix inversion for finding the Kronecker products and the truncation errors are occurred. In this paper, a method for the system analysis of bilinear systems via fast walsh transform is devised. This method requires neither the inversion of large matrices nor the cumbersome procedures for finding Kronecker products. Thus, both the computing time and required memory size can be significantly reduced.

• Journal of Communications and Networks
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• v.13 no.1
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• pp.12-16
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• 2011

In this paper, we construct two families $C^*_m$ and ${\~{C}}^*_m$ of ternary ($2^m$, $3^m$, $2^{m-1}$ ) and ($2^m$, $3^{m+1}$, $2^{m-1}$ ) codes, for m = 1, 2, 3, ${\cdots}$, derived from the corresponding families of modified ternary Jacket matrices. These codes are close to the Plotkin bound and have a very easy decoding procedure.