MATLAB: Is the cosh(Hyperbolic cosine) wrong

cosh function

In recent days, I have confused by the function of cosh(Hyperbolic cosine) in matlab. Suppose the matrix is the following:
S=[ 1.0e-05 *
-0.1293 + 0.0195i  -0.0128 + 0.0079i  -0.0144 + 0.0090i
-0.0141 + 0.0085i  -0.1266 + 0.0197i  -0.0141 + 0.0085i
-0.0144 + 0.0090i  -0.0128 + 0.0079i  -0.1293 + 0.0195i]
The cosh of S with matlab function cosh, the result is:
ans =
 1.0000 - 0.0000i   1.0000 - 0.0000i   1.0000 - 0.0000i
 1.0000 - 0.0000i   1.0000 - 0.0000i   1.0000 - 0.0000i
 1.0000 - 0.0000i   1.0000 - 0.0000i   1.0000 - 0.0000i
In factor, cosh is can be expended by the Maclaurin’s series:
When x is a matrix, the first term of the Maclaurin’s series is unite matrix or identity matrix.
So the result should be :
 ans =
   1.0000 - 0.0000i   0.0000 - 0.0000i   0.0000 - 0.0000i
   0.0000 - 0.0000i   1.0000 - 0.0000i   0.0000 - 0.0000i
   0.0000 - 0.0000i   0.0000 - 0.0000i   1.0000 - 0.0000i

Best Answer

The cosh of S with matlab function cosh, the result is:
ans =
 1.0000 - 0.0000i   1.0000 - 0.0000i   1.0000 - 0.0000i
 1.0000 - 0.0000i   1.0000 - 0.0000i   1.0000 - 0.0000i
 1.0000 - 0.0000i   1.0000 - 0.0000i   1.0000 - 0.0000i
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