I thought that I knew what a unitary transform is, until I started thinking about it.
(2^n-ons are hypercomplex numbers that are related via the 2^n-on construction. Including n=3 the 2^n-on construction gives the same numbers as the Cayley-Dickson construction. From there the 2^n-ons are "nicer".)

I know the following:

Just a note here because I figured it is not clear - I am on vacation these days and, while I continue to post at a regular frequency, I am much more erratic than usual with answering comments in the threads. I would like this to be clear, because I usually do make a point of answering all comments that lend themselves to be answered.

With a slow connection and the need to spend as much time as possible swimming  in the blue waters of Elafonisos, this is bound to be a side effect. I will be back in regular blogging mood by August 10th.