is the cosh(Hyperbolic cosine) wrong?
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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
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Walter Roberson
2015-6-24
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"cosh(X) is the hyperbolic cosine of the elements of X."
In other words, cosh() is applied one by one to the elements of X, independently of the others.
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