I don't have much idea about groups acting on sets and so I have been having trouble trying to approach such kind of questions. If i have group $G$ = $GL$($V$) and the space $S$ of symmetric bilinear forms of V( a finite dimensional $ℝ$-vector space)
The question says the action $G \times S \to S$ can be defined in terms of matrix representation and that it is differentiable. Now this means that the general linear group $GL$($V$) is acting on the space $S$ If i am not wrong. But I am having troubles in understanding the concept of differentiability of this action. And how will i represent this action in terms of matrices ? Edited: symmetric bilinear forms on V can be represented by symmetric matrices but but not sure how ?
any explanations? hints or diagrams will be very helpful.