Suppose $A_1, A_2, \ldots A_k$ are real symmetric (but possibly singular or indefinite) matrices. I want to know whether the system of quadratic equations $$v^T A_i v =0 $$ has a nontrivial solution for $v$.
Is there an efficient way of doing this?
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look through the information on Elimination Theory. It might help. – Betty Mock Oct 24 '13 at 19:35