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I've seen the use of the notation $< \cdot>$ in the context of the vector gradient $\nabla f$.

What does $< \cdot >$ mean? I've also seen the use of $(\cdot)$ in place of it and $(\cdot)$ means just a standard vector. Whereas $<\cdot>$ is often used to denote a linear span.

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$\langle x,y,z\rangle$ means nothing but an element of $\mathbb{R}^3$ in the context of your given link.

The author of that website explains here the distinction of $(\ )$ and $\langle\ \rangle$.

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