diff --git a/Eigen/src/Householder/Householder.h b/Eigen/src/Householder/Householder.h
--- a/Eigen/src/Householder/Householder.h
+++ b/Eigen/src/Householder/Householder.h
@@ -75,8 +75,9 @@
   
   RealScalar tailSqNorm = size()==1 ? RealScalar(0) : tail.squaredNorm();
   Scalar c0 = coeff(0);
+  const RealScalar tol = (std::numeric_limits<RealScalar>::min)();
 
-  if(tailSqNorm == RealScalar(0) && numext::imag(c0)==RealScalar(0))
+  if(tailSqNorm <= tol && numext::abs2(numext::imag(c0))<=tol)
   {
     tau = RealScalar(0);
     beta = numext::real(c0);