Rational power of a positive definite matrix

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q = sym([4 2 ; 2 4]);
f = sqrtm(q)^(-1) - sqrtm(q^(-1));
f should be zero here since q is positive definite.
However, the program yielded a non zero f here. Is this due to the calculation error ? Note that I am using symbolic calculation here so there should be no error at all I assume.

Accepted Answer

John D'Errico
John D'Errico on 13 Feb 2017
Edited: John D'Errico on 13 Feb 2017
Sometimes the answer is just "simple".
simplify(f)
ans =
[ 0, 0]
[ 0, 0]
Symbolic results are not always returned in the most simple possible form.
  1 Comment
Qian Feng
Qian Feng on 13 Feb 2017
Thanks for the suggestion. I should have realized that.

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