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Given a set of multivariate, quadratic, non-homogeneous equations, is there a way to decide how many non-negative roots it have? Some explanations: All the coefficients are real numbers. The number ...

Suppose that eigenvalues of two real square matrix $A$ and $B$ are $1 = \lambda^A_1 > \lambda^A_2 \geq \ldots \geq \lambda^A_n > 0 $ and $1 = \lambda^B_1 > \lambda^B_2 \geq \ldots \geq \...