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From: mrsmith on 16 Jun 2010 04:51
Hi group!

Is the following assertion correct:

There exist two scalar products (.,.) and ((.,.)) in R^m such that for
any pair of linear independent vectors x and y one has (x,y)>0 iff
((x,y))<0.
?
From: José Carlos Santos on 16 Jun 2010 12:06
On 16-06-2010 15:26, David C. Ullrich wrote:

>> Is the following assertion correct:
>>
>> There exist two scalar products (.,.) and ((.,.)) in R^m such that for
>> any pair of linear independent vectors x and y one has (x,y)>0 iff
>> ((x,y))<0.
>> ?
>
> Hint:<x,x> .

Did you miss the "linear independent vectors" part of the problem?

Best regards,

Jose Carlos Santos
From: hagman on 16 Jun 2010 12:34
On 16 Jun., 18:06, José Carlos Santos <jcsan...(a)fc.up.pt> wrote:
> On 16-06-2010 15:26, David C. Ullrich wrote:
>
> >> Is the following assertion correct:
>
> >> There exist two scalar products (.,.) and ((.,.)) in R^m such that for
> >> any pair of linear independent vectors x and y one has (x,y)>0 iff
> >> ((x,y))<0.
> >> ?
>
> > Hint:<x,x>  .
>
> Did you miss the "linear independent vectors" part of the problem?
>
> Best regards,
>
> Jose Carlos Santos

The hint was only an approximation.
Better hint: <x, approximately x>

hagman
From: hagman on 16 Jun 2010 12:35
On 16 Jun., 18:34, hagman <goo...(a)von-eitzen.de> wrote:
> On 16 Jun., 18:06, José Carlos Santos <jcsan...(a)fc.up.pt> wrote:
>
>
>
> > On 16-06-2010 15:26, David C. Ullrich wrote:
>
> > >> Is the following assertion correct:
>
> > >> There exist two scalar products (.,.) and ((.,.)) in R^m such that for
> > >> any pair of linear independent vectors x and y one has (x,y)>0 iff
> > >> ((x,y))<0.
> > >> ?
>
> > > Hint:<x,x>  .
>
> > Did you miss the "linear independent vectors" part of the problem?
>
> > Best regards,
>
> > Jose Carlos Santos
>
> The hint was only an approximation.
> Better hint:  <x, approximately x>
>
> hagman

.... and of course the truth of the statement depends on m
From: David C. Ullrich on 16 Jun 2010 12:41
On Wed, 16 Jun 2010 17:06:15 +0100, Jos� Carlos Santos
<jcsantos(a)fc.up.pt> wrote:

>On 16-06-2010 15:26, David C. Ullrich wrote:
>
>>> Is the following assertion correct:
>>>
>>> There exist two scalar products (.,.) and ((.,.)) in R^m such that for
>>> any pair of linear independent vectors x and y one has (x,y)>0 iff
>>> ((x,y))<0.
>>> ?
>>
>> Hint:<x,x> .
>
>Did you miss the "linear independent vectors" part of the problem?

Yes, although as hagman points out it doesn't matter - I could
claim it was only a hint, not a solution. (Of course that would be a
fib...)

>Best regards,
>
>Jose Carlos Santos

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