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Norms as a Function of p Are Linearly Independent in Finite Dimensions
The American Mathematical Monthly
Vol. 119, No. 7 (August‒September 2012), pp. 601-603
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.119.07.601
Page Count: 3
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Abstract We show that there are no non-trivial linear dependencies among p-norms of vectors in finite dimensions that hold for all p. The proof is by complex analytic continuation.
Copyright the Mathematical Association of America 2012