Let \(n\) be a positive integer and let \(a\) be a complex number. Prove that \(a^n=1\) if and only if there are invertible \(n\times n\) complex matrices \(X,Y\) such that \[ YX=aXY. \]
Invertible matrices with $YX=aXY$ exist iff $a^n=1$
P-BKS19-6A
- Area
- Prelim
- Seen at
- BERKELEY
- Years
- 2019
- Status
- draft