Skip to main content
2 of 4
added 10 characters in body
Denis Serre
  • 52.3k
  • 10
  • 146
  • 300

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: $$\begin{cases} X\cdot trace=Det \\X\cdot Det=-trace \end{cases}$$ where $Det$ is determinant?

Ali Taghavi
  • 356
  • 8
  • 31
  • 123