 
Summary: Noname manuscript No.
(will be inserted by the editor)
On Bar Frameworks, Stress Matrices and Semidefinite
Programming
A. Y. Alfakih
Aug 6, 2009. Revised March 14, 2010
Abstract A bar framework G(p) in rdimensional Euclidean space is a graph G on the
vertices 1, 2, . . . , n, where each vertex i is located at point pi
in Rr
. Given a framework
G(p) in Rr
, a problem of great interest is that of determining whether or not there
exists another framework G(q), not obtained from G(p) by a rigid motion, such that
qi
 qj
2
= pi
 pj
2
for each edge (i, j) of G. This problem is known as either the
