[Pw_forum] Coordinate transorms: Crystal to Cartesian and back

[Gabriele Sclauzero]

Kostyantyn Borysenko wrote:
> 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

Dear Kostyantyn,

    maybe the linear algebra I'm speaking about is not the same you learnt...
I believe mine works!

GS


> 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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