Dear Arti,
The sign | | in this case means "determinant", not "absolute value".
Upon expanding that 3x3 determinant by Cramer's rule you get a cubic
polynomial in lambda, which can indeed be solved by Cardan's formula. You
should definitely give it a try. Condensed algebraic notation like | | can
be confusing.
Best of luck,
Gerard.
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On Sun, Jul 08, 2007 at 01:06:51PM -0600, [EMAIL PROTECTED] wrote:
> Hello all,
>
> I am trying to understand how the anisotropic displacement parameters
> output by shelxl in the form U11 U22 U33 U23 U13 U12 relate with the
> displacement in the x, y and z directions of say an ellipsoid in ORTEP.
> So far I tried to find the eigenvalues for the matrix using the relationship
>
> |Ucart - (lambda)I|=0
>
> where lambda would give the eigenvalues along the three principal axis. In
> the above relationship, I assumed the | | to stand for absolute value and
> used just basic algebra to find the value of lambda, which will be the
> inverse matrix for Ucart in this case. I used the reference
>
> On the handling of atomic anisotropic displacement
> parameters
> R. W. Grosse-Kunstleve* and P. D. Adams
> J. Appl. Cryst. (2002). 35, 477±480
>
> to look up the above relationship. In the paper it is mentioned that
>
> |Ucart - (lambda)I|=0
>
> is solved using Cardan's formula.
>
> So I probably oversimplified my solution and have it wrong.
>
> Can anyone please help me on this? Is there a simple way of knowing the
> displacement along a major axis on the ellipsoid itself in terms of
> Angstrom?
> Thank you.
>
> Arti S. Pandey
> Chemistry and Biochemistry
> Montana State University
> Bozeman,MT 59717
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