I am calculating the eigen value of 2x2 matrix symbolically, and checking whether the two eigen values are negative or not using isAlways, here is the code
syms a d g positive
Am =[(12*g)/(d*(7*d + 24*g)), (a*d^2 + 6*a*g*d + 144*g + 9*a*g)/(12*d*(7*d + 24*g));...
-(4*g*(3*d^2 + 14*d + 12*g))/(d^3*(7*d + 24*g)), -(672*d*g + a*d^4 + 36*a*g^2 + 144*d^2*g + 576*g^2 + 42*a*d*g + 18*a*d^2*g + 6*a*d^3*g)/(12*d^3*(7*d + 24*g))]
I am getting A1(1) to be positive and A1(2) to be negative.
When I am checking numerically by assiginig the value of a, d, g I am getting both the eigen values to be negative and the literature form where I took this expression says that for positive value of a, d, g the matrix Am has negative real eigen values.
Is there anything wrong with my code or is it the limition of isAlways command???
If suppose there are some parametric region where the eigen value are positive or say negative how to find out?
Any help please.