From: Andy Latto <andy.latto@pobox.com>
To: math-fun <math-fun@mailman.xmission.com> Sent: Thursday, November 22, 2012 9:01 AM Subject: Re: [math-fun] complex hermitian matrix
On Thu, Nov 22, 2012 at 11:41 AM, Warren Smith <warren.wds@gmail.com> wrote:
As Andy pointed out, the probability measure should be invariant under arbitrary unitary transformations, i.e. M -> U M U^(-1).
No, I'm saying something much stronger. The probability measure should be invariant under arbitrary translations,
M -> MN, with N hermitian. This, together with the requirements that the entire group has measure 1 and that open sets are measureable, uniquely determines a measure.
Andy
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But Hermitian matrices do not make a group. (AB)* = B* A* = BA, which need not equal AB. -- Gene