- #1
jimbo11
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I'm wrestling with this problem and I'd appreciate any pointers anyone can give me. (I've tried Google, but no luck.)
I'm trying to figure out the total mass, with respect to the Haar measure I guess, that's accounted for by a definite subset of [itex]\mathbf{SO}(n)[/itex]. Specifically, working in [itex]\mathbb{R}^n[/itex], we're given a minimum and maximum rotation between each pair of coordinates: say [itex]\theta_{12} \in \left[ \underline{a}, \overline{a} \right] [/itex], [itex] \theta_{13} \in \left[ \underline{b}, \overline{b} \right][/itex] and so on. If we call the rectangle bounded by those limits [itex] \Theta [/itex], I need to work out [itex] \int_\Theta dO(\vec{\theta})[/itex].
I'm a novice at this, so any suggestions would be gratefully received!
I'm trying to figure out the total mass, with respect to the Haar measure I guess, that's accounted for by a definite subset of [itex]\mathbf{SO}(n)[/itex]. Specifically, working in [itex]\mathbb{R}^n[/itex], we're given a minimum and maximum rotation between each pair of coordinates: say [itex]\theta_{12} \in \left[ \underline{a}, \overline{a} \right] [/itex], [itex] \theta_{13} \in \left[ \underline{b}, \overline{b} \right][/itex] and so on. If we call the rectangle bounded by those limits [itex] \Theta [/itex], I need to work out [itex] \int_\Theta dO(\vec{\theta})[/itex].
I'm a novice at this, so any suggestions would be gratefully received!