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From: Pascal on 21 Jun 2010 18:21
Hi,

I have an oblique coordinate system (a,b,c) and its associated dual
space (a*,b*,c*).
I have an orthonormal coordinate system (x,y,z).

I have defined a matrix G that converts coordinates from (a,b,c) to
(x,y,z).

I also have a doubly contravariant tensor U in (a,b,c) that I would
like to express in (x,y,z) which I called V.

I naively thought that V = G U G^t (^t is the transpose) (like a
symmetry operation) but I need to use V = (G D) U (G D)^t instead.

D is a diagonal 3x3 matrix with the diagonal elements [a*,b*,c*] and
zero otherwise.

Does anyone have an idea where D comes from ?
The field where I am using these calculations is crystallography.

Pascal
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