  We consider two classes of actions on $\mathbb{R}^n$ - one continuous and one
discrete. For matrices of the form $A = e^B$ with $B \in M_n(\R)$, we consider
the action given by $\gamma \to \gamma A^t$. We characterize the matrices $A$
for which there is a cross-section for this action. The discrete action we
consider is given by $\gamma \to \gamma A^k$, where $A\in GL_n(\R)$. We
characterize the matrices $A$ for which there exists a cross-section for this
action as well. We also characterize those $A$ for which there exist special
types of cross-sections; namely, bounded cross-sections and finite measure
cross-sections. Explicit examples of cross-sections are provided for each of
the cases in which cross-sections exist. Finally, these explicit cross-sections
are used to characterize those matrices for which there exist MSF wavelets with
infinitely many wavelet functions. Along the way, we generalize a well-known
aspect of the theory of shift-invariant spaces to shift-invariant spaces with
infinitely many generators.
