Consider two vectors $x\in\mathbb{R}^n$ and $y\in\mathbb{R}^n$. Obviously, $x^\top y = 0$ implies that $x$ and $y$ are orthogonal. Now, let $A\in\mathbb{R}^{n \times n}$ be a matrix. What is the meaning of $$x^\top A y = 0$$? Does this imply orthogonality of $x$ and $y$ with respect to something?
2026-04-25 16:12:39.1777133559
Orthogonality with respect to a matrix
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