• 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 Communications and Networks
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• v.3 no.4
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• pp.361-364
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• 2001

Over an additive abelian group G of order g and for a given positive integer $\lambda$, a generalized Hadamard matrix GH(g, $\lambda$) is defined as a gλ$\times$gλ matrix[h(i, j)], where 1 $\leq i \leqg\lambda and 1 \leqj \leqg\lambda$, such that every element of G appears exactly $\lambd$atimes in the list h($i_1, 1) -h(i_2, 1), h(i_1, 2)-h(i_2, 2), …, h(i_1, g\lambda) -h(i_2, g\lambda), for any i_1\neqi_2$. In this paper, we propose a new method of expanding a GH(g^m, \lambda_1) = B = [B_{ij}] over G^m$ by replacing each of its m-tuple B_{ij} with B_{ij} + GH(g, $\lambda_2) where m = g\lambda_2. We may use g^m/\lambda_1 (not necessarily all distinct) GH(g, \lambda_2$)s for the substitution and the resulting matrix is defined over the group of order g.

• 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.11
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• pp.2512-2520
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• 1997

The classes of Reverse Jacket matrix [RJ]$_{N}$ and the corresponding Restclass Reverse Jacket matrix ([RRJ]$_{N}$) are defined;the main property of [RJ]$_{N}$ is that the inverse matrices of them can be obtained very easily and have a special structure. [RJ]$_{N}$ is derived from the weighted hadamard Transform corresponding to hadamard matrix [H]$_{N}$ and a basic symmertric matrix D. the classes of [RJ]$_{2}$ can be used as a generalize Quincunx subsampling matrix and serveral polygonal subsampling matrices. In this paper, we will present in particular the systematical block-wise extending-method for {RJ]$_{N}$. We have deduced a new orthorgonal matrix $M_{1}$.mem.[RRJ]$_{N}$ from a nonorthogonal matrix $M_{O}$.mem.[RJ]$_{N}$. These matrices can be used to develop efficient algorithms in IMT2000 signal processing, multidimensional subsampling, spectrum analyzers, and signal screamblers, as well as in speech and image signal processing.gnal processing.g.

• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.633-639
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• 2000

Let $A=(a_{ij}\ and\ B=(b_{ij}\ be\ n\times\ n$ complex matrices and let A$\bigcirc$B denote the Hadamard product of A and B, that is $AA\circB=(A_{ij{b_{ij})$.We conjecture a permanental analog of Oppenheim's inequality and verify it for n=2 and 3 as well as for some infinite classes of matrices.

• Journal of Communications and Networks
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• v.13 no.3
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• pp.211-213
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• 2011

In this paper, we propose a key agreement protocol using Sylvester Hadamard matrices. Users obtain their common key by using a matrix shared in advance. Matrix construction is very simple, and the computation is quite fast. The proposal will be useful for communication between two users, especially for those having low computing power.

• Journal of electromagnetic engineering and science
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• v.7 no.1
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• pp.28-34
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• 2007

In this paper, we present a quasi-Jacket block matrices over binary matrices which all are belong to a class of cocyclic matrices is the same as the Hadamard case and are useful in digital signal processing, CDMA, and coded modulation. Based on circular permutation matrix(CPM) cocyclic quasi block low-density matrix is introduced in this paper which is useful in coding theory. Additionally, we show that the fast algorithm of quasi-Jacket block matrix.

• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.641-649
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• 2017

For partitioned matrices, the Khatri-Rao product is viewed as a generalized Hadamard product. In this paper we present Oppenheim's and Schur's determinantal inequalities for the Khatri-Rao product of two positive semidefinite matrices.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.673-683
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• 2009

We point out: to make Hermtian matrices A and B satisfy Styan matrix inequality, the condition "positive definite property" demanded in the present literatures is not necessary. Furthermore, on the premise of abandoning positive definite property, we derive Styan matrix inequality of Hadamard product for inverse Hermitian matrices and the sufficient and necessary conditions that the equation holds in our paper.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.47 no.5
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• pp.10-15
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• 2010

Good performance of spectral-amplitude-coding optical CDMA can be obtained using codes based upon Hadamard matrices, but Hadamard codes have very restrictive code lengths of $2^n$. In this paper a new code family, namely extended Hadamard code, is proposed to relax the code length restriction and the number of simultaneous users. The improved performance of the proposed system is analysed with the consideration of phase-induced intensity noise(PIIN).