What is the map $\text{GL}_n(\mathbb{C}) \to \text{GL}_n(\mathbb{C}) \times \text{GL}_n(\mathbb{C})$ named in the title? I guess it has something to do with the polar decomposition, but I can't manage to write down something that looks algebraic (which of course the sought-after map must be). Part of the trouble is that I don't understand how complexification is functorial in general.
2026-03-30 06:49:23.1774853363
Complexification of the inclusion $\text{U}_n\subset \text{GL}_n(\mathbb{C})$
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