Can I say that the norm of a component of the vector is smaller than the norm of the whole vector? (in this case the gradient)
$$\|v_x\| < \|\operatorname{grad} v\|$$
2026-03-29 04:11:52.1774757512
Norm, gradient, vector
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Less than or equal to, but yes. Consider $v =\langle 1,0\rangle$. This has a 2-Norm of 1 and an infinity Norm (largest single component) of 1 as well.