diag problem while substracting

my rho total is a square matrix, and when I do that:

 diag(rho_total-1)

it gives me

 1.0e-15 *

   0.444089209850063
   0.444089209850063
  -0.111022302462516
  -0.111022302462516
  -0.222044604925031
   0.666133814775094

why is that e-15 there?

Answer 1

[James Tursa]

It's just a display format thing. It means each number shown is actually multiplied by 1.0e-15

E.g.,

>> [1 2 3]
ans =
     1     2     3
>> [1e-16 2e-16 3e-16]
ans =
  1.0e-015 *
    0.1000    0.2000    0.3000

So the diagonal numbers of rho_total you show in your post were actually pretty close to 1, since the difference between them and 1 is close to eps(1).

[James Tursa]

Consider this example:

>> [1 1;1 1]
ans =
     1     1
     1     1
>> [1-eps 1;1 1+eps]
ans =
    1.0000    1.0000
    1.0000    1.0000
>> diag([1-eps 1;1 1+eps] - 1)
ans =
  1.0e-015 *
   -0.2220
    0.2220

E.g., you can get those trailing .0000 digits printed when the numbers are not exactly integers. Subtracting the integer reveals the difference between what is really there and what is printed to the screen. In your case, whatever floating point calculations were done to produce rho_total did not result in exact 1's on the diagonal. They were very close (relative to 1), but not exactly 1.