Let $G$ be the special linear group $SL(2,F_q)$ where $F_q$ is a finite field of order $q$. Is it true that all matrices of the upper triangular group (or a conjugate of it) of $G$ have a common eigenvector?
All matrices of the upper triangular group (or a conjugate of it) have a common eigenvector
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linear-algebra
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0What about the first standard basis vector? – 2017-01-01
1 Answers
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It's not clear what you mean by "or a conjugate of it". However, every upper-triangular matrix has the standard basis vector $(1,0,\dots,0)$ as an eigenvector.