1 citations · 2 across the 34 of their papers we have counts for
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Completely Positive Biquadratic Tensors
Liqun Qi, Chunfeng Cui, Haibin Chen +1
In this paper, we systemically introduce completely positive biquadratic (CPB) tensors and copositive biquadratic tensors. We show that all weakly CPB tensors are sum of squares te…
Strongly Positive Semi-Definite Tensors and Strongly SOS Tensors
Liqun Qi, Chunfeng Cui
We introduce {odd-order} strongly PSD (positive semi-definite) tensors which map real vectors to nonnegative vectors. We then introduce odd-order strongly SOS (sum-of-squares) tens…
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…
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…
A Genuine Extension of The Moore-Penrose Inverse to Dual Matrices
Chunfeng Cui, Liqun Qi
The Moore-Penrose inverse is a genuine extension of the matrix inverse. Given a complex matrix, there uniquely exists another complex matrix satisfying the four Moore-Penrose condi…
Dual Number Matrices with Primitive and Irreducible Nonnegative Standard Parts
Liqun Qi, Chunfeng Cui
In this paper, we extend the Perron-Frobenius theory to dual number matrices with primitive and irreducible nonnegative standard parts. One motivation of our research is to conside…
Eigenvalues and Jordan Forms of Dual Complex Matrices
Liqun Qi, Chunfeng Cui
Dual complex matrices have found applications in brain science. There are two different definitions of the dual complex number multiplication. One is noncommutative. Another is com…