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Ali Taghavi
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A vector field $X$ on $GL(n,\mathbb{R})$ with $\begin{cases} X.trace=Det \\X.Det=-trace \end{cases}$

Is there a vector field $X$ on $M_n(\mathbb{R})$ or $GL(n,\mathbb{R})$ with the following condition: $$\begin{cases} X.trace=Det \\X.Det=-trace \end{cases}$$ where $Det$ is determinant?

Ali Taghavi
  • 356
  • 8
  • 31
  • 123