Square root of a matrix

I encountered a problem when I try to compute the square root of a positive definite matrix

syms x real

mi = [1; exp(x); exp(2*x); exp(3*x); exp(-x)];

F = vpa(simplify(int(mi*mi',x,-10,0), 'Steps', 100)); Fs = sqrtm(F);

The problem here is Fs should be a symmetric matrix but Fs- Fs' here is not a zero matrix.

I have tried to use symbolic calculation instead of vpa but it seems that it requires a very long time to compute.

Is there any way that Fs can be computed without destroying its symmetric structure ?

Answer 1

[Matt J]

You can post-correct the asymmetry as follows,

Fs=(Fs+Fs.')/2