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THE DOUBLE DETERMINANT OF VANDERMONDE'S TYPE OVER quaternion field

Applied Mathematics and Mechanics(English Edition) 1999年第9期20卷 1046-1053页

作者：侯仁民赵旭强王亮涛 Department of Mathematics and Information Science Yantai University Yantai P R China

Based on the double determinant theory the problem about the determinant of Vandermonde's type over quaternion field is studied, and a necessary and sufficient condition that this double determinant is not equal to ze... 详细信息

关键词： quaternion field double determinant Vandermonde determinant

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GENERALIZED DIAGONALIZATION OF MATRICES OVER quaternion field

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Applied Mathematics and Mechanics(English Edition) 1999年第11期20卷 1297-1304页

作者：姜同松陈丽 Department of Mathematics Linyi Teachers College Linyi P R China Department of Physics Linyi Teachers College Linyi P R China

A concept of [GRAPHICS] diagonalization matrix over quaternion field is given, the necessary and sufficient conditions for determining whether a quaternion matrix is a [GRAPHICS] diagonalization one are discussed, and... 详细信息

关键词： complex quaternion ring quaternion field matrix diagonalization matrix

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The Subpositive Definite Solution of the Unified Algebraic Lyapunov Equation over quaternion field

The Subpositive Definite Solution of the Unified Algebraic L...

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第三十届中国控制会议

作者： HUANG Jing-Pin College of Mathematics and Computer Science,Guangxi University for Nationalities,Nanning 530006,P.R.China

By using the structure-preserving property of complexification operator of the quaternion matrices,some necessary and sufficient conditions for the existence of subpositive definite solution of the unified algebraic Lyapunov equation AX+XA+θA XA=-Q over quaternion field are *** the same time,we construct iterative algorithm to find subpositive definite solution of this matrix equation,the convergence of the iteration is analyzed,and the method for selecting sampling period is ***,a numeral example shows the feasibility of the method.

关键词： quaternion field Unified Algebraic Lyapunov Equation Subpositive Definite Solution Iterative Sampling Period

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四元数体上矩阵的Jordan标准形

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Northeastern Mathematical Journal 1994年第1期10卷 18-24页

作者：黄礼平

et H(F) be the quaternion field over a real ciooed field F. By the method of subfield transformation, this poper prove that every n ×n matrix over H(F) is similar to a Jordan canonical form,and the Jordan canonital form is unique. By using Jordan Canonical form, this peper gets some important properties of similarity tramformetion of metrices over H(F)

关键词： Jordan Canonical Form Matrix quaternion field Real Closed field Method of Subfield Transformation

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Cyclic Solution and Optimal Approximation of the quaternion Stein Equation

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Journal of Applied Mathematics and Physics 2023年第11期11卷 3735-3746页

作者： Guangmei Liu Yanting Zhang Yiwen Yao Jingpin Huang College of Mathematics and Physics Guangxi Minzu University Nanning China

In this paper, two different methods are used to study the cyclic structure solution and the optimal approximation of the quaternion Stein equation AXB - X = F . Firstly, the matrix equation equivalent to the target structure matrix is constructed by using the complex decomposition of the quaternion matrix, to obtain the necessary and sufficient conditions for the existence of the cyclic solution of the equation and the expression of the general solution. Secondly, the Stein equation is converted into the Sylvester equation by adding the necessary parameters, and the condition for the existence of a cyclic solution and the expression of the equation’s solution are then obtained by using the real decomposition of the quaternion matrix and the Kronecker product of the matrix. At the same time, under the condition that the solution set is non-empty, the optimal approximation solution to the given quaternion circulant matrix is obtained by using the property of Frobenius norm property. Numerical examples are given to verify the correctness of the theoretical results and the feasibility of the proposed method. .

关键词： quaternion field Stein Equation Cyclic Matrix Complex Decomposition Real Decomposition Optimal Approximation

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The Hankel Matrix Solution to a System of quaternion Matrix Equations

The Hankel Matrix Solution to a System of Quaternion Matrix ...

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第32届中国控制与决策会议

作者： Yun Wang Jingpin Huang Hao Xiong Shanshan Zhang College of Science Guangxi University for Nationalities

The solution of matrix equations and the optimal approximation problem play an important role in linear optimal control,parameter identification,structural vibration,aviation and other *** matrix is kind of matrix with special structure and wide *** this paper,the problem of Hankel constraint solution to the system [AXB CXD]=[E F] over quaternion field is *** using the representation of vectors of a Hankel matrix and Kronecker product of matrices,a constrained problem will be transformed into an unconstrained *** the necessary and sufficient conditions for the equations with Hankel solution as well as the expression of general solution are ***,when the solution set is nonempty,by using invariance of Frobenius norm of orthogonal matrix product,the optimal approximation solution with minimal Frobenius norm for a given Hankel matrix is ***,two numerical examples is provided to verify the algorism.

关键词： quaternion field quaternion Matrix Equations Hankel Matrix Kronecker Product Optimal Approximation

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Inverse Arnoldi Algorithm for Construction of Tridiagonal quaternion Matrix

Inverse Arnoldi Algorithm for Construction of Tridiagonal Qu...

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第30届中国控制与决策会议

作者： Jingpin Huang Liman Chen Cong Shen College of Science Guangxi University for Nationalities Guangxi Key Laboratories of Hybrid Computation and Integrated Circuit Design Analysis

An inverse spectra problem which has an important significance in the control field is discussed, that is, find an irreducible tridiagonal quaternion matrix T, such that T has the given distinct nonzero eigenvalues 1{ }n i i =λ and a right eigenpairs 1 1（λ,α）. In this paper, we use inverse Arnoldi algorithm for an unitary similarity matrix and construct the appropriate similarity transformation, an irreducible tridiagonal quaternion matrix T with given conditions is obtained. At the same time, two numerical examples checks the method’s feasibility and precision.

关键词： quaternion field tridiagonal matrix right eigenpairs nonzero eigenvalues inverse Arnoldi algorithm

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