• Korean Journal of Mathematics
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• 제16권4호
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• pp.565-571
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• 2008

In this paper we present some trace inequalities for positive definite matrices in statistical mechanics. In order to prove the method of the uniform bound on the generating functional for the semi-classical model, we use some trace inequalities and matrix norms and properties of trace for positive definite matrices.

• 호남수학학술지
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• 제38권4호
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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.

• 호남수학학술지
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• 제45권3호
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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.

• Journal of applied mathematics & informatics
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• 제38권1_2호
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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.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1992년도 하계학술대회 논문집 A
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• pp.296-298
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• 1992

Presented in this paper is a generalized norm bound for the continuous and discrete algebraic Riccati equations. The generalized norm bound provides a lower bound of the Riccati solutions specified by any kind of submultiplicative matrix norms including the spectral, Frobenius and $\ell_1$ norms.

• 대한수학회보
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• 제48권5호
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• pp.1093-1103
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• 2011

We give the characterizations of the classes of matrix trans-formations ($m(\phi),{\ell}_p$), ($n(\phi),{\ell}_p$) ([5, Theorem 2]), (${\ell}_p,m(\phi)$) ([5, Theorem 1]) and (${\ell}_p,n(\phi)$) for $1{\leq}p{\leq}{\infty}$, establish estimates for the norms of the bounded linear operators defined by those matrix transformations and characterize the corresponding subclasses of compact matrix operators.

• 한국수학교육학회지시리즈A:수학교육
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• 제19권2호
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• pp.29-30
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• 1981

• 대한수학회논문집
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• 제33권3호
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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.

• 정보보호학회논문지
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• 제18권4호
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• pp.53-68
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• 2008

실용적인 프라이버시 보호 기술 중의 하나인 행렬 기반 랜덤화 기법에 대하여 세밀한 분석을 실시한다. 최적의 변환 행렬을 찾기 위한 프라이버시 손상 관점의 요구조건 및 정확성 측도로 제안된 행렬의 조건수 개념과 연관된 파라미터들간의 관계를 이론적으로 규명한다. 행렬 기반의 대표적 알고리즘인 랜덤 대치 기법의 효율적인 구현을 위하여 데이터 재구축 과정에서 필요한 역행렬을 간단히 구하는 공식을 제시하고, 행렬의 노름에 따른 변환 행렬의 조건수와 변환된 분포의 기댓값 및 분산을 계산함으로써 표준오차와 파라미터들 간의 관계식을 도출한다. 또한, 랜덤 대치 기법을 구현하여 다양한 시뮬레이션을 실시함으로써 이론적으로 얻은 결과를 실험적으로 검증한다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1999년도 제14차 학술회의논문집
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• pp.129-132
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• 1999

This paper deals with the optimal filtering problem constrained to input noise signal corrupting the measurement output for linear discrete-time systems. The transfer matrix H$_2$and/or H$_{\infty}$ norms are used as criteria in an estimation error sense. In this paper, the mixed $H_2/H_{\infty}$ filtering Problem in lineal discrete-time systems is solved using the LMI approach, yielding a compromise between the H$_2$and H$_{\infty}$ filter designs. This filter design problems we formulated in a convex optimization framework using linear matrix inequalities. A numerical example is presented.