Solving Antisymmetric Matrix: Rx=zy & Ry=-zx

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Homework Statement


Hi, If I have an antisymmetric matrix R, how might I show that there are real 3D vectors x and y and some real number z such that
Rx=zy and Ry=-zx?
Thanks!

Homework Equations


Rx=zy and Ry=-zx

The Attempt at a Solution


I know that it is true intuitively because it is like a rotation matrix... but am not quite sure how to show it...
 
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Hi, problem solved! :)
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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