Arcadian Functor

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Marni D. Sheppeard

Sunday, March 16, 2008

M Theory Lesson 169

Thanks to Steven H. Cullinane for this diagram of Hamilton's quaternions, the whirligigs. Recall that this plane over the three element finite field $\mathbb{F}_3$ arises in the $d = 3^{n}$ MUB problem, associated to the Fourier transform of the $p = 3$ mass matrices.

3 Comments:

Blogger CarlBrannen said...

Okay, I get it. The 2x2 matrices, acting on the 2x1 vectors, do the arrow transformations (when working in the field with three elements 0, 1, -1).

March 16, 2008 7:21 PM  
Anonymous Steven H. Cullinane said...

I fear my title for this picture, "Hamilton's whirligigs," was misleading. The quaternions are, of course, Hamilton's, but the pictures of the quaternion actions on 3x3 arrays are mine.

March 16, 2008 11:24 PM  
Blogger Kea said...

Oh, thanks Steven! All the better.

March 17, 2008 9:17 AM  

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