How many eigenvalues of a random
matrix are real?
>> e=eig(randn(7))
e =
   1.9771
   1.3442
   0.6316
  -1.1664 + 1.3504i
  -1.1664 - 1.3504i
  -2.1461 + 0.7288i
  -2.1461 - 0.7288i
3 real                            1 real                            5 real
7x7 random Gaussian