165 citations · 445 across the 26 of their papers we have counts for
9 papers · 1 filter
Nondegeneracy of eigenvectors and singular vector tuples of tensors
Shenglong Hu
In this article, nondegeneracy of singular vector tuples, Z-eigenvectors and eigenvectors of tensors is studied. They have found many applications in diverse areas. The main result…
Tensor Norm, Cubic Power and Gelfand Limit
Liqun Qi, Shenglong Hu, Xinzhen Zhang +1
We establish two inequalities for the nuclear norm and the spectral norm of tensor products. The first inequality indicates that the nuclear norm of the square matrix is a matrix n…
Biquadratic Tensors, Biquadratic Decomposition and Norms of Biquadratic Tensors
Liqun Qi, Shenglong Hu, Xinzhen Zhang
Biquadratic tensors play a central role in many areas of science. Examples include elasticity tensor and Eshelby tensor in solid mechanics, and Riemann curvature tensor in relativi…
Spectral Norm and Nuclear Norm of a Third Order Tensor
Liqun Qi, Shenglong Hu
The spectral norm and the nuclear norm of a third order tensor play an important role in the tensor completion and recovery problem. We show that the spectral norm of a third order…
A Necessary and Sufficient Condition for Existence of a Positive Perron Vector
Shenglong Hu, Liqun Qi
In 1907, Oskar Perron showed that a positive square matrix has a unique largest positive eigenvalue with a positive eigenvector. This result was extended to irreducible nonnegative…
Relations of the Nuclear Norms of a Tensor and its Matrix Flattenings
Shenglong Hu
For a -tensor of dimensions , we show that the nuclear norm of its every matrix flattening is a lower bound of the tensor nuclear norm, and which in tur…