The order-$n$ minors of certain $(n+k)\times n$ matrices

Abstract

We determine sufficient conditions for certain classes of $(n+k)\times n$ matrices $E$ to have all order-$n$ minors to be nonzero. For a special class of $(n+1)\times n$ matrices $E,$ we give the formula for the order-$n$ minors. As an application we construct subspaces of $\C^m \otimes \C^n$ of maximal dimension, which does not contain any vector of Schmidt rank less than $k$ and which has a basis of Schmidt rank $k$ for $k=2,3,4$.

14 pages. arXiv admin note: text overlap with arXiv:1804.04204. We fix the gap in the proof and put the detailed. The final version will be appeared in the journal