55 citations · 214 across the 36 of their papers we have counts for
5 papers · 1 filter
Topology of tensor ranks
Pierre Comon, Lek-Heng Lim, Yang Qi +1
We study path-connectedness and homotopy groups of sets of tensors defined by tensor rank, border rank, multilinear rank, as well as their symmetric counterparts for symmetric tens…
Hankel tensor decompositions and ranks
Jiawang Nie, Ke Ye
Hankel tensors are generalizations of Hankel matrices. This article studies the relations among various ranks of Hankel tensors. We give an algorithm that can compute the Vandermon…
New classes of matrix decompositions
Ke Ye
The idea of decomposing a matrix into a product of structured matrices such as triangular, orthogonal, diagonal matrices is a milestone of numerical computations. In this paper, we…
Every matrix is a product of Toeplitz matrices
Ke Ye, Lek-Heng Lim
We show that every n-by-n matrix is generically a product of [n/2] + 1 Toeplitz matrices and always a product of at most 2n+5 Toeplitz matrices. The same result holds true if the w…
On the geometry of tensor network states
J. M. Landsberg, Yang Qi, Ke Ye
We answer a question of L. Grasedyck that arose in quantum information theory, showing that the limit of tensors in a space of tensor network states need not be a tensor network st…