Strongly Independent Matrices and Rigidity of $\times A$-Invariant Measures on $n$-Torus

6 Aug 2019 · Huichi Huang, Hanfeng Li, Enhui Shi, Hui Xu ·

We introduce the concept of strongly independent matrices over any field, and prove the existence of such matrices for certain fields and the non-existence for algebraically closed fields. Then we apply strongly independent matrices over rational numbers to obtain a measure rigidity result for endomorphisms on $n$-torus.