occasional meanderings in physics' brave new world
- Name: Kea
- Location: New Zealand
Marni D. Sheppeard
Tuesday, May 05, 2009
Last time we saw how a symmetric magic matrix could be decomposed into one three dimensional and one two dimensional piece. Sadly, AF has neglected to mention some lovely properties of Combescure matrices, acting via conjugation. For example, on the two dimensional circulant piece we have so $R_3$ simply permutes the indices. And recall that $R_3$, being a $1$-circulant, fixes any $1$-circulant. On three dimensional $2$-circulants it acts like the basic permutation operator $(231)$. That is, $R_3$ naturally encodes several permutation actions.