A dictionary, or not?
I realized that I’ve been attempting to do greedy approximation in the set of symmetric matrices using the “dictionary” 
without checking that this is indeed a dictionary: is the closure of the span of this set the set of all symmetric matrices?
As someone just pointed out, this is obviously not the case, since the diagonals of symmetric rank one sign matrices are constant. Darn (and don’t I feel stupid). Ok, I guess I’ll have to settle for greedy approximation with the dictionary 
Maybe that original dictionary of symmetric rank one sign matrices is a dictionary for the Hilbert space of symmetric matrices with constant diagonals? I don’t have time to think about that. Doesn’t seem bloody useful: you’d only be able to apply this to covariance matrices of equivariant variables.
Possibly relevant posts:
- Is uniqueness important? (2/17/2010)
- Two linear algebra puzzlers (3/23/2010)
- A way not to get sign decompositions (2/26/2010)
norm and the 
norm