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The one parameter group of the the general linear group $\gamma =e^{tA}$ where $A$ is a $n\times n$ matrix.

I am looking for a geometric or mental picture of what this is.

If not with GL, is there a subgroup of GL where the one-parameter group can be visualized? For instance, does the one-parameter subgroup of SO(3,1) corresponds to the path of a particle in spacetime?

Or is it the one-parameter subgroup of SO(3,1) multiplied by an initial position 4-vector, that represents to path of this particle in spacetime away from the initial position?

Anon21
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  • A one-parameter subgroup is not a particle trajectory but more a coordinate-change trajectory. One way to visualize is to depict the effect on Cartesian space, which includes (very particular paths of) rotation, shearing, stretching, boosting, and compositions of these. – Andrew D. Hwang Jun 19 '22 at 23:05
  • @AndrewD.Hwang Thank you - crystal clear. Returning to the particle picture: Is it possible to connect this path, to the path of a particle? – Anon21 Jun 20 '22 at 00:00

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