Stata FAQ
How do I do elementwise operations on a matrix?

Here is a small (3x3) Stata example of a matrix in which each element is exponentiated.  You can generalize this example to any kind of elementwise matrix operation.

matrix x = (1,2,3\2,3,4\3,4,5)
matrix list x

symmetric x[3,3]
    c1  c2  c3
r1   1
r2   2   3
r3   3   4   5

matrix y = x /* create y */

/* begin loop */
local i=1
while `i'<=3 {
  local j=1
  while `j'<=3 {
    matrix y[`i' , `j'] = exp(x[`i' , `j'])
    local j = `j' + 1
  }
   local i = `i' + 1
} /* end loop */

/* matrix y is now the exponentiated matrix */
matrix list y

symmetric y[3,3]
           c1         c2         c3
r1  2.7182818
r2  7.3890561  20.085537
r3  20.085537   54.59815  148.41316