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<DIV><SPAN class=370384316-22052009><FONT face=Arial size=2>Dear Andrea and
Gabriele,</FONT></SPAN></DIV>
<DIV><SPAN class=370384316-22052009><FONT face=Arial
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=370384316-22052009><FONT face=Arial size=2>Thank you for your
responses. </FONT></SPAN></DIV>
<DIV><SPAN class=370384316-22052009><FONT face=Arial
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=370384316-22052009><FONT face=Arial size=2>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</FONT></SPAN></DIV>
<DIV><SPAN class=370384316-22052009><FONT face=Arial size=2>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.</FONT></SPAN></DIV>
<DIV><SPAN class=370384316-22052009><FONT face=Arial size=2>I still can't see
any false logic in my derivation.</FONT></SPAN></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV align=left>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN lang=EN-US
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial; mso-ansi-language: EN-US">Best
regards,<?xml:namespace prefix = o ns =
"urn:schemas-microsoft-com:office:office" /><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN lang=EN-US
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial; mso-ansi-language: EN-US"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN lang=EN-US
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial; mso-ansi-language: EN-US">Kostyantyn
Borysenko</SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN lang=EN-US
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial; mso-ansi-language: EN-US"></SPAN><FONT
face=Arial size=2>Department of Electrical and Computer Engineering <BR>North
Carolina State University<BR></FONT></P></DIV></BODY></HTML>