  We propose a very simple preprocessing algorithm for semidefinite
programming. Our algorithm inspects the constraints of the problem, deletes
redundant rows and columns in the constraints, and reduces the size of the
variable matrix. It often detects infeasibility. Our algorithm does not rely on
any optimization solver: the only subroutine it needs is Cholesky
factorization, hence it can be implemented with a few lines of code in machine
precision. We present computational results on a set of problems arising mostly
from polynomial optimization.
