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> All norms on finite-dimensional vector spaces are equivalent How are you going to tell me that an L1 norm is equivalent to an L2 norm, for example?
by TreeRingCounter 4y ago
> All norms on finite-dimensional vector spaces are equivalent
How are you going to tell me that an L1 norm is equivalent to an L2 norm, for example?
- brewmarche 4y agoThis is a standard result which you can look up in most text books, or here on StackExchange: https://math.stackexchange.com/questions/57686/understanding-of-the-theorem-that-all-norms-are-equivalent-in-finite-dimensional https://math.stackexchange.com/questions/57686/understanding... In the end it doesn’t whether we go to infinity in one norm or the other. Note that I am talking about finite dimensions, so I guess you didn’t mean the L^p norms or \ell^p for integrable functions or sequences but the finite-dimensional p-norms.
- TreeRingCounter 4y agoThis theorem is completely irrelevant - the equivalence relation described by the theorem does not imply an equivalence between ordinal relationships imposed by different choice of norm. Also, "tails" isn't the same as "at infinity".