What are the metric spaces ?

[BAT_MAN]

metric vs matrices

please help me in understanding the difference between metrin and matrices in linear algebra and please gave me some notes relating to metrices i will be greatful

 

[Kral]

Re: metric vs matrices

BAT_MAN,
Your question is not clear. Could you re-post with correct, consistent spelling, and a short example?
Regards,
Kral

 

[maharshi_qis]

Re: metric vs matrices

question is not clear..
any way metric is some unit..where is matrices sre part of mathematics..

 

[BAT_MAN]

Re: metric vs matrices

sorry my question was metric spaces what are they ????? what are their relation with the matrices and vector spaces.

 

[mayyan]

Re: metric vs matrices

Metric spaces are a basic term in functional analysis. It play a similar role to the real line R in calculus ( generelize R).

The reason for this generalization is:
1) this way we can deal with essential insted of going into detail.
2) people noticed that problems from diferent fields share the same features. by generalisation unify our aproch towards such problems
3) abbstruction is the simplest and most economical way to deal with mathemtical problems

( people who hate math want angry with the last note )


Definition: Metric Space

a metric space is a pair (X,d) where X is a set and d is a metric on X. ( d is also called the distance function and it generelize the way distance is nade in cacluluse)
the metric is defind acxiomaticaly in this fashion:

1. d(x,y)=0 <=> x=y
2. d(x,y)=d(y,x)
3. d(x,y) <= d(x,z) + d(z,y)
4. d is real, finite and unegetive

( where x,y,z are member of X )

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the relation between metric spaces and a vector space is noremed spaces. which takes the algeblic concepts of of vector spacese with the geometric concepts of metric spaces. this is done by defining a norm on a vector space.

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if you need to know the subject what i said above it only the motivation. You will need to get a good real / functional analysis book and do some reading.