Doubly stochastic averaging of a monovarying bilinear form: $\sum_{k,l} a_k S_{kl} b_l \le \sum_k a_k b_k$

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Doubly stochastic averaging of a monovarying bilinear form: $\sum_{k,l} a_k S_{kl} b_l \le \sum_k a_k b_k$ · Prove2Me