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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…
Eigenvalues and Singular Values of Dual Quaternion Matrices
Liqun Qi, Ziyan Luo
The poses of robotics in time points may be represented by an dual quaternion matrix. In this paper, we study the spectral theory of dual quaternion matrices.…
Eigenvalues and Singular Value Decomposition of Dual Complex Matrices
Liqun Qi, Ziyan Luo
We introduce right eigenvalues and subeigenvalues for square dual complex matrices. An dual complex Hermitian matrix has exactly right eigenvalues and subeigenvalu…
A Note on Quaternion Skew-Symmetric Matrices
Liqun Qi, Ziyan Luo
The product of a complex skew-symmetric matrix and its conjugate transpose is a positive semi-definite Hermitian matrix with nonnegative eigenvalues, with a property that each dist…