• Honam Mathematical Journal
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• v.45 no.3
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• pp.418-432
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• 2023

In this study, we consider the Hankel and Gram matrices which are defined by the elements of special number sequences. Firstly, the eigenvalues, determinant, and norms of the Hankel matrix defined by special number sequences are obtained. Afterwards, using the relationship between the Gram and Hankel matrices, the eigenvalues, determinants, and norms of the Gram matrices defined by number sequences are given.

• Kyungpook Mathematical Journal
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• v.13 no.1
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• pp.11-20
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• 1973

• Journal of the Korea Institute of Information Security & Cryptology
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• v.14 no.6
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• pp.105-110
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• 2004

MAC is used for data origin authentication or message integrity protection. In Crypto'03 Cary and Venkatesan introduced new MAC based on unimodular matrix groups. It is to encrypt messages using private keys and to encrypt them again using public keys which are matrices whose determinants are $\pm$1. These matrices have property called k-invertible. This k effects on the collision probability of this new MAC. The smaller k is, the less collisions occur. Cary shows 6-invertible matrices, and 10-invertible matrices whose components are only 1, 0, -1. In this paper we figure out sufficient conditions about choosing 4 matrices among special 22 matrices. Also, we introduce 5-invertible matrices whose components are 1, 0, -1. Those have better efficiency and security.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.665-675
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• 2017

Several properties of the sequence generated from a kind of Danzer matrices were examined and proved using already known facts about the Chebyshev polynomials. Asymptotic behavior of our interest sequence also discussed.

• Korean Journal of Mathematics
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• v.15 no.2
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• pp.177-183
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• 2007

In this paper, we study the Riordan matrices with the A-sequence (1,1,...,1,0,...) where 1's appear in m times. As a result, we obtain new Riordan matrices and give their lattice path interpretations.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.583-602
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• 1995

With the theory of a certain type of orders in a Quaternion algebra, we construct Brandt matrices and theta series. As a application, we calculate the class number of a certain type of orders in a Quanternion algebra with the trace formular of Brandt matrices.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.519-529
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• 2002

We investigate implementation of the determinantal representation of generalized inverses for complex and rational matrices in the symbolic package MATHEMATICA. We also introduce an implementation which is applicable to sparse matrices.

• Korean Journal of Mathematics
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• v.11 no.2
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• pp.155-160
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• 2003

In this paper we shall study the limit of the doubly stochastic matrices obtained from Boolean regular matrices.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.269-273
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• 1997

We show that each element in the semigroup $S_n$ of all $n \times n$ non-singular stochastic totally positive matrices is generated by the infinitesimal elements of $S_n$, which form a cone consisting of all $n \times n$ Jacobi intensity matrices.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.1021-1027
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• 2013

We consider right and left Fredholm operator matrices of the form $\[\array{A&C\\T&S}\]$, which are linear and bounded on the Banach space $Z=X{\oplus}Y$.