Timeline for Does there exist a continuous path between two sets of oriented basis for a vector space out of a collection of subspaces?
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Nov 18, 2018 at 13:06 | comment | added | erz | For the variation of the problem with $\mathbb{R}$ replaced with $\mathbb{C}$ (not sure it helps): consider the set $S$ of all tuples $v_1,...,v_n$, where $v_i\in V_i$. Clearly, $S$ is a vector space, and so we can identify it with a linear subspace of $\mathbb{C}^{n^2}$. Then $\det(v_1,...,v_n)$ is a polynomial of a degree at most $n$ on $S$, who is linearly isomorphic to $\mathbb{C}^{mn}$. Since the zero-set of an analytic function does not separate $\mathbb{C}^{mn}$, it follows that the bases for a connected set. | |
| Nov 14, 2018 at 23:20 | history | asked | user1101010 | CC BY-SA 4.0 |