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Results tagged with orthogonal-matrices
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user 9471
An orthogonal matrix is an invertible real matrix whose inverse is equal to its transpose.
12
votes
Real orthogonal and sign
Here's a simple argument that this is false for $n > 2$.
In dimension $n$ there are $2^{n}$ orthants, $2^{n-1}$ if one considers them modulo sign. A pair of antipodal orthants means a pair of orthant …
- 2,139
6
votes
Accepted
Upper bound on the sectional curvature of the orthogonal group
The $n = 3$ case is a straightforward computation using the identification of the cross product on $\mathbb{R}^{3}$ with the Lie bracket on $\mathfrak{so}(3)$. Namely, defined $\hat{x}:\mathbb{R}^{3} …
- 2,139