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Triangular Decomposition of Third Order Hermitian Tensors
Liqun Qi, Chunfeng Cui, Ziyan Luo
We define lower triangular tensors, and show that all diagonal entries of such a tensor are eigenvalues of that tensor. We then define lower triangular sub-symmetric tensors, and s…
Even Order Pascal Tensors are Positive Definite
Chunfeng Cui, Liqun Qi, Yannan Chen
In this paper, we show that even order Pascal tensors are positive definite, and odd order Pascal tensors are strongly completely positive. The significance of these is that our in…
Moore Determinant of Dual Quaternion Hermitian Matrices
Chunfeng Cui, Liqun Qi, Guangjing Song +1
In this paper, we extend the Chen and Moore determinants of quaternion Hermitian} matrices to dual quaternion Hermitian matrices. We show the Chen determinant of dual quaternion He…
Non-convex Pose Graph Optimization in SLAM via Proximal Linearized Riemannian ADMM
Xin Chen, Chunfeng Cui, Deren Han +1
Pose graph optimization (PGO) is a well-known technique for solving the pose-based simultaneous localization and mapping (SLAM) problem. In this paper, we represent the rotation an…
Eigenvalues of Dual Hermitian Matrices with Application in Formation Control
Liqun Qi, Chunfeng Cui
We propose a supplement matrix method for computing eigenvalues of a dual Hermitian matrix, and discuss its application in multi-agent formation control. Suppose we have a ring, wh…
Spectral Properties of Dual Unit Gain Graphs
Chunfeng Cui, Yong Lu, Liqun Qi +1
In this paper, we study dual quaternion and dual complex unit gain graphs and their spectral properties in a unified frame of dual unit gain graphs. Unit dual quaternions represent…
Unit Dual Quaternion Directed Graphs, Formation Control and General Weighted Directed Graphs
Liqun Qi, Chunfeng Cui, Chen Ouyang
We study the multi-agent formation control problem in a directed graph. The relative configurations are expressed by unit dual quaternions (UDQs). We call such a weighted directed…