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Results tagged with orthogonal-matrices
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user 149789
An orthogonal matrix is an invertible real matrix whose inverse is equal to its transpose.
24
votes
2
answers
877
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Simple conjecture about rational orthogonal matrices and lattices
The following conjecture grew out of thinking about topological phases of matter. Despite being very elementary to state, it has evaded proof both by me and by everyone I've asked so far. The conjectu …
13
votes
Accepted
Simple conjecture about rational orthogonal matrices and lattices
Proof
Let $R$ be any matrix. We have the obvious exact sequence
$$ 0 \longrightarrow\mathbb{R}^N \xrightarrow[\left(\begin{matrix} I \\ R \end{matrix}\right)]{} \mathbb{R}^N \oplus \mathbb{R}^N \xri …