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Adjprog Crackedexe Epson L120 Software,. support for Epson TX Epson DO TX Epson LA Epson L405 Epson L335 Epson L320 Epson L220. Join us today to download the latest free software.Q:
$\operatorname{U}(n)$: How to write this subgroup as product of subgroups isomorphic to $\mathbb{R}$?
So, let’s say I have a subgroup of $\operatorname{U}(n)$, is there an easy way to write it as product of subgroups isomorphic to $\mathbb{R}$? I’m assuming those are only $U(1)$ and $U(n-1)$?
I’m using this notation, which denotes the cosets of this group as $G/H$, where the preimage of $H$ by $\phi$ is the equivalence class.
A:
You have the right idea. The subgroup $\mathrm{U}(n-1)$ is embedded into $\mathrm{U}(n)$ by $\phi: A \mapsto A^*$ and the subgroup $\mathrm{U}(1)$ is embedded by $\phi: A \mapsto \det A$, where $A^*$ is the transpose and $\det$ is the determinant.
In your notation, the right coset $G/H$ consists of matrices $A$ that have the same determinant as $A^*$, and the left coset $H A$ is the same as $A^*$, which gives your result.
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