# Positive definite solution

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dab483 on 23 Nov 2011
i need to solved for different values of gama until its lowest value, which gives a positive definite solution for P is found, so i am using all(eig(P)>0) like the equation below:
is this right?
gama=100000;
for i=1:2000;
P = inv(inv(P)+M'*inv(R)*M-gama^(-2)*eye(4));
E=eig(P_cov);
if all(eig(P))>0) %%(all eigenvalues must be positive)
gama=gama/2;
else
break;
end
end
P = inv(inv(P)+M'*inv(R)*M-gama^(-2)*eye(4));
is this correct?

Walter Roberson on 23 Nov 2011
If the eigenvalues are all positive, you change gama, exiting the loop when they are not all positive. That means that at the end the gama you get out will be such that the eigenvalues are not all positive. This does not satisfy the stated conditions.
dab483 on 24 Nov 2011
Thank you. It satisfy the stated conditions.

Sean de Wolski on 23 Nov 2011
Use a second variable and only update it if the eigenvalues are all positive. When you exit the loop it will be the last set of all positive eigenvalues.
dab483 on 23 Nov 2011
Can you show it a litle bit.. i'm blank right now.