# Tagged Questions

50 views

### Are periodic points dense in the unitary group?

In $U(1) = \{z \in \mathbb{C} : |z| = 1\}$, it is well known and easy to see that the set of $z$ so that $z^n = 1$ for some $n \in \mathbb{Z}_+$ are dense. Does this fact generalize to the group ...
108 views

### orthogonal group of a quadratic vector space

I am reading about the orthogonal group $O(V)$ of a real finite dimensional quadratic vector space $(V,Q)$ with $Q$ nondegenerate. By definition O(V)=\{f:V\mapsto V |\quad Q(f(v))=Q(v) \quad \forall ...
259 views

### Normal subgroups of the Special Linear Group

What is some normal subgroups of SL(2, R)? I tried to check SO(2, R), UT(2, R), linear algebraic group and some scalar and diagonal matrices, but still couldn't come up with any. So can anyone give ...
Let $V$ be a finite-dimensional real linear space, and let $K$ be a compact subgroup of $GL(V)$ (with the usual topology); then is there a basis of $V$ such that every $f\in K$ is an orthogonal matrix ...
Let $K$ be a topological field. Let $V$ be a topological vector space over $K$ (if it makes things convenient, you may assume it is finite dimensional). Naive Question: Is there a canonical way of ...