On completion of a linearly independent set to a basis with shifts of a fixed vector

Marek Rychlik

Let $\mathbb{F}$ be an infinite field. Let $n$ be a positive integer and let $1\le d\le n$. Let ${\vec{f}}_1,{\vec{f}}_2,\dots ,{\vec{f}}_{d-1}\in {\mathbb{F}}^n$ be $d-1$ linearly…