A linear action refers to a way in which a Lie group acts on a vector space such that the group elements transform vectors linearly. This means that if you have a vector and apply a group element to it, the result is still a vector in the same space, and this transformation respects both addition and scalar multiplication. Linear actions are essential in understanding how Lie groups interact with vector spaces and play a crucial role in the study of representations and orbits.
congrats on reading the definition of linear action. now let's actually learn it.