2010-04-27 13:29, Gonzalo Tornaria skrev:
2010/4/27 Johan Grönqvist<johan.gronqv...@gmail.com>:
Those did not even mention that
there is an alternative definition of norm used in number theory.
Here it is: http://en.wikipedia.org/wiki/Field_norm
Thanks. Now I learned something new.
The norm on complex numbers is not consistent with viewing the complex
numbers as a two-dimensional real vector space, according to the definitions
mentioned above.
One caveat: "the" norm of a two-dimensional real vector space is not
canonical. In contrast, the norm of a two-dimensional field extension
is uniquely defined.
True, but the argument was not about the particular choice of norm, but
the property
norm(a*v) == abs(a) * norm(v) [for any scalar a and any vector v]
required for any vector-space norm. That property does not seem to hold
for the field norm.
Regards
Johan
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