[Pw_forum] Coordinate transorms: Crystal to Cartesian and back

[Kostyantyn Borysenko]

Dear Andrea and Gabriele,
 
Thank you for your responses. 
 
2Gabriele: I beleive there is a mistake in your first step. When you start
with v_cart = A*v_cryst, you try to use the property (C*D)' = D' * C', which
is true for the product of two matrices. In our case we have a product of
matrix A and vector v_cryst. So you will get v_cart' = v_cryst' * A
Also, in my original question I meant that vector v and matrix W represent
some physical values that have correspongly vector and tensor nature. If one
wants to change the coordinate system where these values are defined, one
needs to perform an appropriate transformation. In our case this
transformation is determined by the matrices A and B constructed from
lattice vectors in real and reciprocal space. So if you want to transform a
vector using transformation matrix T, you will get an equation of the form:
v_new = T*v_old; and if you transform a matrix the corresponding equation
will look like W_new = T' * W_old * T.  But in the context of this
discussion, the product of the form (v' * W * v) is irrelevant.
I still can't see any false logic in my derivation.
 

Best regards,

 

Kostyantyn Borysenko

Department of Electrical and Computer Engineering 
North Carolina State University


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