[Rd] eigenvector dimname convention?

[Spencer Graves]

      What are reasonable conventions for dimnames for eigenvectors? 

      The standard 'eigen' function discards dimnames. 

      If a matrix X is symmetric (and rownames = colnames), it seems 
more sensible to assign rownames(eigen(X)$vectors) <- rownames(X).  The 
eigenvalues seem different, so I'm inclined to assign names like ev1, 
ev2, ..., to the eigenvectors and use those names for the columns of 
eigen(...)$vectors. 

      However, this analysis does not apply if rownames != colnames.  
What should be done in that case?  The 'solve' function uses a 
convention that might help here: 

 tst <- matrix(1:4, 2, dimnames=list(LETTERS[1:2], letters[3:4]))
 > tst
  c d
A 1 3
B 2 4

solve(tst)
   A    B
c -2  1.5
d  1 -0.5

      Tentative conclusion:  If rownames != colnames (or the matrix is 
not symmetric), then dimnames(eigen(X)$vectors) = dimnames(X).  That's 
because X = (vectors %*% values %*% solve(vectors)).  If desired, the 
eigenvalues can be assigned names matching colnames(X). 

      Does this make sense? 

      I ask, because I'm writing a function 'EIGEN' as a wrapper for 
'eigen' that tries to preserve dimnames.  This analysis suggests that 
how dimnames are assigned is at least partly a matter of convention 
rather than mathematics. 

      Thanks,
      Spencer Graves