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Interpretation of determinants on commutative rings
In real Euclidian space, the result of the determinant can be interpreted as the oriented volume of the image of the unit cube under an invertible linear map.
This interpretation conceptually depends ...
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Why is $O(n;k)$ not connected, and has four connected components? [closed]
Why is $O(n;k)$ not connected and has four connected components when $nk\ge 1$?
Here $O(n;k) =\{A\in GL(n+k,\mathbb{R}) \mid A^{T}GA=G\}$
where
$G=\begin{pmatrix}
1&&&&&\\
&\...
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