论文标题
双元基质矩阵的正确特征值及其广义倒置的最小原理
Minimax principle for right eigenvalues of dual quaternion matrices and their generalized inverses
论文作者
论文摘要
双偶四合一可以代表3D空间中的刚体运动，并在机器人技术，3D运动建模和控制以及计算机图形中发现了广泛的应用。在本文中，我们为一组双季化媒介介绍了三种不同的右线性独立性，并研究了一组双重四基因矢量和双重四元基质矩阵的一些相关基本特性。我们提出了一个最小值原理，用于双季节赫尔米尼亚矩阵的正确特征值。基于新建立的凯奇 - 雪Warz的不平等和双重媒介的不平等和双重四元基质矩阵的奇异价值分解，我们提出了对双重四基因矩阵奇异值的重要不平等。最终，我们介绍了双重四元基质矩阵的广义倒数的概念，并为双重四基因矩阵提供了必要和足够的条件，使其成为另一种双重四元基质矩阵的四种类型的广义倒置之一。
Dual quaternions can represent rigid body motion in 3D spaces, and have found wide applications in robotics, 3D motion modelling and control, and computer graphics. In this paper, we introduce three different right linear independency for a set of dual quaternion vectors, and study some related basic properties for the set of dual quaternion vectors and dual quaternion matrices. We present a minimax principle for right eigenvalues of dual quaternion Hermitian matrices. Based upon a newly established Cauchy-Schwarz inequality for dual quaternion vectors and singular value decomposition of dual quaternion matrices, we propose an important inequality for singular values of dual quaternion matrices. We finally introduce the concept of generalized inverse of dual quaternion matrices, and present the necessary and sufficient conditions for a dual quaternion matrix to be one of four types of generalized inverses of another dual quaternion matrix.
