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Is there a transitive Lie group action on the space of matrices with rank bigger than $k$?
$\newcommand{\GL}{\operatorname{GL}}$
Let $H_{>k}$ be the space of real $d \times d$ matrices of rank bigger than $k$, for some fixed $k$. $H_{>k}$ is an open connected submanifold of $ \mathbb{...
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3
votes
0
answers
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Particular decomposition of $SU(n)$
Given $a,b \in \mathfrak{su(n)}$ which generate the full algebra, it is possible to write and $G \in SU(n)$ as:
$G = \exp(\alpha_1 a)\exp(\beta_1 b) \ldots \exp(\alpha_m a)\exp(\beta_m b)$
for some ...
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