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For two given $N\times 1$ vectors $x,y$ , if $||x||_2\geq ||y||_2$, can I say that $||x||_1\geq ||y||_1$? If not give an example. Converse of this question has been asked here.

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Counterexample: $y = \frac{2}{3}[1 \quad 1]^T$, $x = [1 \quad 0]^T$.

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