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a question abt vectors

Posted: Sat Sep 17, 2005 7:41 am
by arif_pasha
there are p (p>=3) vectors. Is it true that we can express every vector as a linear combination of those p vectors which are inside the bounded area of these p vectors?

Posted: Sat Sep 17, 2005 10:00 am
by Dominik Michniewski
You can express any vector as linear combination of any P vectors in P-dimensial space, if these P vectors are:
1. vectors representing axis of space (probably unit vectors like [1,0,0,0])
2. it's possible to represent any axis of space (like above) as linear combination of these P vectors
3. these P vectors must be linear independent, because otherwise we cannot express one or more axis in space as linear combination of these vectors

I don't understand correctly what you mean, but I think that helps you

Best regards
DM