when $x' y >0$ and A is a positive definite matrix, $x' A y > 0$?
Here, x and y is column vector so that $x' y$ is scalar.
2026-03-26 06:07:06.1774505226
when x'y >0 and A is positive definite matrix, x' A y >0?
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No. Namely, $$x=\begin{pmatrix}1 \\ 1\end{pmatrix},\quad y=\begin{pmatrix}2 \\ -1\end{pmatrix},\quad A=\begin{pmatrix}1 & 0\\ 0&5\end{pmatrix}$$