5 papers
Structured matrix factorization length
Jeong-Hoon Ju, Taehyeong Kim
Every (resp. a generic) complex matrix can be expressed as a product of (resp. ) Toeplitz matrices. Motivated by this result, it is natu…
On the computation of tensor functions under tensor-tensor multiplications with linear maps
Jeong-Hoon Ju, Susana Lopez-Moreno
In this paper we study the computation of both algebraic and non-algebraic tensor functions under the tensor-tensor multiplication with linear maps. In the case of algebraic tensor…
The border rank of the determinant tensor is twelve
Jong In Han, Jeong-Hoon Ju, Yeongrak Kim
We show that the border rank of the determinant tensor is at least over , using the fixed ideal theorem introduced by Buczyńska-Buczyński and the meth…
Recursive Koszul flattenings of determinant and permanent tensors
Jong In Han, Jeong-Hoon Ju, Yeongrak Kim
We investigate new lower bounds on the tensor rank of the determinant and the permanent tensors via recursive usage of the Koszul flattening method introduced by Landsberg-Ottavian…
Geometric mean for T-positive definite tensors and associated Riemannian geometry
Jeong-Hoon Ju, Taehyeong Kim, Yeongrak Kim +1
In this paper, we generalize the geometric mean of two positive definite matrices to that of third-order tensors using the notion of T-product. Specifically, we define the geometri…