3 papers
math.AG2025
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…
math.AC2025
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…
math.NA2024
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…