[Pw_forum] Coordinate transorms: Crystal to Cartesian and back

[Kostyantyn Borysenko]

Thanks everyone!
Indeed, I was wrong about transposing the product of matrix and vector.
Silly mistake on my part. 
Like I said in my previous message, I finally was able to reproduce the
expressions in those two subroutines. 
What I didn't understand at first is that if a matrix element depends on
wave vectors k and q (like in our case: <k+q|dV|k>) ,
the transition between cartesian and crystal coordinates actually refers to
transition between basis of Cartesian unit vectors and the basis of unit
vectors in reciprocal lattice. 
So it is a crystal - but in reciprocal space!  Thanks again for your help.
 
Best,
Kostyantyn Borysenko
Department of Electrical and Computer Engineering
NCSU
> all in all, a "N vector" is nothing but a [Nx1] matrix. Its transpose  

> (YES! it is well defined) is a [1xN] matrix. SB



> On May 26, 2009, at 6:58 AM, Huiqun Zhou wrote:



> Kostyantyn , 

>

> The rule for transpose operation applies to not only the product of  

> matrices, but also the

> product of a matrix and a vector.

>

> I believe Gabriele is right.

>

>

> Huiqun Zhou

> @Earth Sciences, Nanjing University, China

>

> 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

>

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