6 citations · 7 across the 9 of their papers we have counts for
9 papers
Grassmann Tensors and their applications in geometry
Changqing Xu, Kaijie Xu, Jun Wang +1
In this paper, we introduce the Grassmann tensor by tensor product of vectors and some basic terminology in tensor theory. Some basic properties of the Grassmann tensors are invest…
Separable symmetric tensors and separable anti-symmetric tensors
Changqing Xu
In this paper, we first introduce the invertibility of even-order tensors and the separable tensors, including separable symmetry tensors and separable anti-symmetry tensors, defin…
High order tensor moments of random vectors
Yan Feng, Shan Song, Changqing Xu
A random vector $\bx\in \R^n$ is a vector whose coordinates are all random variables. A random vector is called a Gaussian vector if it follows Gaussian distribution. These termino…
Random Tensors and their Normal Distributions
Changqing Xu, Kaijie Xu
The main purpose of this paper is to introduce the random tensor with normal distribution, which promotes the matrix normal distribution to a higher order case. Some basic knowledg…
Commutation matrices and Commutation tensors
Changqing Xu
The commutation matrix was first introduced in statistics as a transposition matrix by Murnaghan in 1938. In this paper, we first investigate the commutation matrix which is employ…
On {0,1} CP Tensors and CP Multi-hypergraphs
Changqing Xu, Zhibing Chen, Liqun Qi
A doubly nonnegative matrix can be written as a Gramian matrix, and a completely positive matrix can therefore be written as a Gramian matrix of some nonnegative vectors. In this p…
Completely Positive Tensors and Multi-Hypergraphs
Changqing Xu, Ziyan Luo, Liqun Qi
Completely positive graphs have been employed to associate with completely positive matrices for characterizing the intrinsic zero patterns. As tensors have been widely recognized…
When does cp-rank equal rank?
Wasin So, Changqing Xu
The problem of finding completely positive matrices with equal cp-rank and rank is considered. We give some easy-to-check sufficient conditions on the entries of a doubly nonnegati…
Nonnegative Tensor Factorization, Completely Positive Tensors and an Hierarchical Elimination Algorithm
Liqun Qi, Changqing Xu, Yi Xu
Nonnegative tensor factorization has applications in statistics, computer vision, exploratory multiway data analysis and blind source separation. A symmetric nonnegative tensor, wh…