Rational power of a positive definite matrix

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.

Answer 1

[John D'Errico]

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.

[Qian Feng]

Thanks for the suggestion. I should have realized that.