Re: Real orthogonal group probability question

cgiannel@xxxxxxxxxxx wrote:

Do you mean that f(A(x,e)) for x the 1st unit vector equals

surface area({y on unit sphere: ||y - north pole|| < e}) / surface
area(unit sphere)?

Exactly.

Can you point me to a reference containing a proof?

Probably not, because it is just an exercise to give you the "look and feel"
of the Haar measure. But consider this. If x is the 1sth unit vector,
consider the subset of matrices N such that N(x)=x. What can you say about
that set? Is it a group? Is is a normal subgroup of a given group? Can you
rewrite the integral in function of a certain decomposition?



.

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