Timeline for What is the quantity $\sqrt{\frac{c^2+d^2}{a^2+b^2}}$ of a matrix with determinant one?
Current License: CC BY-SA 4.0
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| Sep 19, 2023 at 11:43 | comment | added | Christophe Leuridan | No. The matrix with rows equal to $(\cosh\theta ~ \sinh \theta)$ and $(\sinh \theta ~ \cosh\theta)$ can be far from being orthogonal although the ratio of their norm is $1$. | |
| Sep 18, 2023 at 23:20 | comment | added | Federico Poloni | Trivial observation: it's the ratio between the norms of the two rows. Intuitively it seems related to the condition number: the larger it is, the further $A$ is from a multiple of an orthogonal matrix. | |
| Sep 18, 2023 at 19:44 | comment | added | Geoff Robinson | I think it's the same as $\frac{\sqrt{1 + (ac+bd)^{2}}}{a^{2}+b^{2}},$ but I do not know any way to attach any meaning to the expression, | |
| Sep 18, 2023 at 18:53 | history | asked | Muzi | CC BY-SA 4.0 |