If $A$ is a positive definite matrix, can we derive a lower bound for the term $x^T A y$, where $x, y$ are two vectors of the following form: $$(x-z)^T A (x-y) \geq \alpha (x-z)^T (x-y), $$ where $\alpha$ is a positive scalar?
2026-03-29 22:12:37.1774822357
Lower bound on a term involving positive definite matrix
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