Given an element $g$ of the orthogonal group $O(n)$, is there a name for the subspace of $R^n$ that's fixed by $g$, and a name for the orthogonal complement of this space? (The la …

I apologize in advance if my question is too elementary for MO. It is a well known fact that the linear algebraic group $G = \mathsf{SO}_n$ is connected, and there exist a few dif …

We would like very much to know the answer to the following question: Let $\|\cdot\|$ be any norm on $\mathbb{Z}^d$ and let $W(\mathbb{Z}^d)$ be the group of all bijections of …

Greetings to all ! Let me first confess that this question was mentionned to me by Bernard Dacorogna, who doesn't sail on MO. Let $A\in M_{2n}(k)$ be an alternate matrix. Say tha …

This is for all that are interested in classical groups and their representations. We are investigating the following situation: Let $V$ be $d$-dimensional $k$-vector space (where …

Hello, I am looking for information about the symplectic groups $Sp_{2m}(2)$ as permutation group acting on quadratic forms. Consider the block matrices \[e=\begin{pmatrix}0&1 …

In ${\bf M}_n(\mathbb R)$, let us consider the usual operator norm $$\|A\|=\sup\frac{\|Ax\|}{\|x\|},$$ where $\|x\|$ is the Euclidian norm. The closed unit ball $B$ is the set of …

I was recently taking some notes on the Cartan-Dieudonné theorem: if $(V,q)$ is a nondegenerate quadratic space of finite dimension $n$ over a field of characteristic not $2$, then …