4 papers · 1 filter
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…