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Topic: Multiplicative Seminorms
Replies: 3   Last Post: Aug 31, 2005 1:57 PM

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Robert Low

Posts: 1,458
Registered: 12/6/04
Re: Multiplicative Seminorms
Posted: Aug 31, 2005 1:57 PM
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G. A. Edgar wrote:
> Barbato <mauriziobarbato@aruba.it> wrote:
>>I'm thining about the following problem:
>>let R(n,n) be the algebra of nxn real matrices.
>>Does there exist a "non-trivial" seminorm in R(n,n), such that for every A, B
>>in R(n,n) we have:
>>||AB||=||A||*||B||? (the "trivial" seminorm is defined by ||A||=0 for every A
>>||in R(n,n)).
>>Thank you very much for your help.
>>Maury
> absolute value of determinant?

That violates the triangle inequality: if
we're in R(n,n) (n>1) then

|det(I+I)|=2^n > 2 = |det(I)|+|det(I)|

Or doesn't a seminorm have to satisfy the
triangle inequality?

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