The tensor rank decomposition problem consists of recovering the unique set
of parameters representing a robustly identifiable low-rank tensor when the
coordinate representation of the tensor is presented as input. A condition
number for this problem measuring the sensitivity of the parameters to an
infinitesimal change to the tensor is introduced and analyzed. It is
demonstrated that the absolute condition number coincides with the inverse of
the least singular value of Terracini's matrix. Several basic properties of
this condition number are investigated.Comment: 45 pages, 4 figure
