• 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.

• Journal of the Institute of Electronics and Information Engineers
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• v.51 no.5
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• pp.3-10
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• 2014

In this paper we review the typical Toeplitz matrices and block circulant matrices, and propose the a circulant Hadamard matrix which is consisted of +1 and -1, but its structure is different from typical Hadamard matrix. The proposed circulant Hadamard matrix decreases computational complexities to $Nlog_2N$ additions through high speed algorithm compare to original one. This matrix is able to be applied to Massive MIMO channel estimation, FIR filter design, amd signal processing.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.593-605
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• 2015

In this study, we define r-circulant, circulant, Hankel and Toeplitz matrices involving the integer sequence with recurrence relation U_n = pU_n-1 + U_n-2, with U₀ = a, U₁ = b. Moreover, we obtain special norms of above mentioned matrices. The results presented in this paper are generalizations of some of the results of [1, 10, 11].

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.695-704
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• 2018

In this paper, firstly we compute the spectral norm of g-circulant matrices $C_{n,g}=g-Circ(c_0,c_1,{\cdots},c{_{n-1}})$, where $c_i{\geq}0$ or $c_i{\leq}0$ (equivalently $c_i{\cdot}c_j{\geq}0$). After, we compute the spectral norms, determinants and inverses of the g-circulant matrices with the Fibonacci and Lucas numbers.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.317-324
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• 2001

A Cayley graph of a finite group G is called normal edge-transitive if its automorphism group has a subgroup which both normalized G and acts transitively on edges. In this paper, we consider Cayley graphs of finite cyclic groups, namely, finite circulant graphs. We characterize the normal edge-transitive circulant graphs and determine the normal edge-transitive circulant graphs of prime power order in terms of lexicographic products.

• Kyungpook Mathematical Journal
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• v.28 no.1
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• pp.45-50
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• 1988

Circulant and multiblock circulant matrices have many important applications, and therefore their inverses are of considerable interest. A simple recursive algorithm is presented to compute the inverse of a multiblock circulant matrix. The algorithm only uses complex variables, roots of unity and normal matrix/vector operations.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.81-96
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• 2004

The level-m scaled circulant factor matrix over the complex number field is introduced. Its diagonalization and spectral decomposition and representation are discussed. An explicit formula for the entries of the inverse of a level-m scaled circulant factor matrix is presented. Finally, an algorithm for finding the inverse of such matrices over the quaternion division algebra is given.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1441-1456
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• 2017

We consider a 3-dimensional Riemannian manifold M with a circulant metric g and a circulant structure q satisfying $q^3=id$. The structure q is compatible with g such that an isometry is induced in any tangent space of M. We introduce three classes of such manifolds. Two of them are determined by special properties of the curvature tensor. The third class is composed by manifolds whose structure q is parallel with respect to the Levi-Civita connection of g. We obtain some curvature properties of these manifolds (M, g, q) and give some explicit examples of such manifolds.

• Honam Mathematical Journal
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• v.38 no.4
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• pp.725-738
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• 2016

In this paper, the explicit determinants of the circulant and negacyclic matrix involving Tetranacci sequence $M_n$ and Companion-Tetranacci sequence $K_n$ are expressed by using only Tetranacci sequence $M_n$ and Companion-Tetranacci sequence $K_n$. Also euclidean norms and spectral norms of circulant and negacyclic matrices have been obtained.

• The KIPS Transactions:PartA
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• v.14A no.4
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• pp.249-254
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• 2007

In this paper, we consider the embedding problem of postorder Fibonacci circulant. We show that Fibonacci linear array, Fibonacci mesh, Fibonacci tree, Fibonacci cubes and Hypercube are a subgraph of postorder Fibonacci circulant.