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Results tagged with linear-algebra
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user 67031
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
15
votes
$SO(m+1)$-equivariant maps from $S^m$ to $S^m$
$G$ acts transitively on $S^m$, so if you know the image of the north pole $N = (0,\dotsc,0,1)$, there is for every other point $p\in S^m$ an element $g\in S^m$ such that $p = g\cdot (0,\dotsc,0,1)$. …
7
votes
1
answer
360
views
Symplectic structure vanishing simultaneously on two totally real subspaces
Let $L_1,L_2$ be two $\mathbb{R}$-linear subspaces of $\mathbb{C}^n$ that are both totally real, that is, $$L_j \cap \bigl(i\cdot L_j\bigr) = \{0\}$$ and $$\dim_{\mathbb{R}} L_j = \dim_{\mathbb{C}} \m …