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A. Mathematical Preliminaries
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A. Mathematical Preliminaries
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A.2 Means
A.
1
Norms
Definition A..
1
(Norm) A normed space
is a vector space
(over a field
) with a norm
such that for all
and
,
,
.
Definition A..
2
(Equivalent Norms) Two norms
and
on a vector space
are called equivalent if there are positive numbers
and
such that
Remark.
Equivalent norms on
define the same topology on
.
Theorem A..
3
(Equivalence of Norms) All norms on a finite dimensional normed space are equivalent.
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A. Mathematical Preliminaries
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A. Mathematical Preliminaries
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A.2 Means
Clemens Heitzinger 2003-05-08