There is another characterization of positive definiteness:
for all column vectors .
This might be a little easier to use.
I have this problem that I really can't solve.
For which s and t do A and B have all eigenvalues λ > 0 (therefore positive definite)?
I tried to use the characteristic polynomial but I can't solve it since it's third degree. I also tried Cholesky decomposition for symmetric matrices, but the elements of the matrices are too complicated to be used in a useful way.
Could someone help me?