Hi
This is a linear-algebra question (with structural biology hidden
behind...).
I came across the following matrix equation :
A = S X
where :
* A, S and X are real square matrices
* A is a known (constant) matrix
* S and X are unknown
* S must be symmetric
* X must be orthogonal
I know there exist at least one solution to the equation --the polar
decomposition of A-- and that this decomposition may not be unique (if A
is singular).
However, since S is not required to be positive-semidefinite (like in a
polar decomposition), I was wondering if :
* further solutions may exist
* there is a criterion to establish the existence /number of these
solutions
* there is a practical way of calculating them
--
Stefano Trapani
Maître de Conférences
http://www.cbs.cnrs.fr/index.php/fr/personnel?PERS=Stefano%20Trapani
-------------------------------------
Centre de Biochimie Structurale (CBS)
29 rue de Navacelles
34090 MONTPELLIER Cedex, France
Tel : +33 (0)4 67 41 77 29
Fax : +33 (0)4 67 41 79 13
-------------------------------------
Université de Montpellier
CNRS UMR 5048
INSERM UMR 1054
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