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So what do you recommend to resolve this!!!!!!?
So you say that a vector 'v' with distance 0 does not mean it is a zero
vector.
Consider this example. The metric space (S, sigma). S is a set of
sequence of observations.
s1=[1, 2, 3, 3, 4, 3, 3, 3, 3, 4, 5, 6, 7, 8, 9] belongs to S.
s2=[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] belongs to S too.
s1+s2=[2, 3, 4, 4, 5, 4, 4, 4, 4, 5, 6, 7, 8, 9, 10] also belongs to S.
sigma is the standard deviation of the observations.
Now,
sigma(s1)=sigma1
sigma(s2)=0
sigma(s1+s2)=sigma(s1)
sigma(s1+s2, s1)=sigma(s1)-sigma(s1+s2)=0
1. Does not this mean that s1+s2 equals s1 (according to the metric)!?
2. If this is true, doesnot this mean that s2 is a ZERO vector!?
3. Consider s3=[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],
Doesnot s1+s3 equal s1 (according to the metric)!?
Now we have two zeros s2, s3!? Am right or missing something!?
Thanks alot for time, Bye.
On Oct 31, 3:04 pm, Virgil <vir...@xxxxxxxxxxx> wrote:
> In article <1162268294.384599.319...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
>
>
>
> "m7ossny" <m7os...@xxxxxxxxx> wrote:
> > Hi,
>
> > I am not an Algebra Guru and have some question. Consider a metric
> > space of vectors 'V' with a distance function 'd'. The vector space 'V'
> > has a primary operator '+'. The problem is that I have to define zero
> > vector where
>
> > 1. d(ZERO)=0.
> > 2. v + ZERO =ZERO + v = v (for all 'v' in 'V')
>
> > Some times the '+' operator and 'd' function are complex enough that
> > there might be more than one zero vector (a subset of vectors that all
> > has absolute distance equal to zero). Some other cases there is a zero
> > vector for each vector.
>
> > Does this sound right!? Or am I missing something!?There is no more that
> > one zero-vector per vector space, with or without
> a metric.
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