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User:Polnasam

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Well, I signed in because I saw a clear case of vandalism in one page that, apparently, had been around for several months. As a regular user of WP, I felt the need to start contributing back, whence, signing in and removing that edit.

Any way, I think now I might stay around and see if I can really contribute with anything useful.


Metric tensor

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This is a coordinate-free, algebraic characterization of a (pseudo-) metric tensor[1] .

Dual space and forms

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Let denote a finite-dimensional linear space over a field (e.g., ), with vectors , where summation over repeated indices (Einstein convention) is assumed and the set is a basis of . The dual of the space, denoted as , is the vectorial space of Linear functionals or forms (see also one-form), denoted as , that map into , i.e.,


where will be called the duality product in .
is the basis of called the dual basis of if it satisfies that

.



Polnasam (talk) 21:11, 24 June 2011 (UTC)

References

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  1. ^ Tarantola, Albert (2006). Elements for Physics: Quantities, Qualities and Intrinsic Theories. Berlin, Heidelberg: Springer-Verlag. p. 278. ISBN 3-540-25302-5.