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Jul 16, 2018 at 5:45 comment added Sean Eberhard Nice, thank you. I regard the unit-norm and arbitrary-norm problems as equivalent, because $V$ contains an element of norm $1$ if and only if $xV$ contains an element of norm $N(x)$ for $x \neq 0$.
Jul 15, 2018 at 22:22 history answered Felipe Voloch CC BY-SA 4.0