diff --git a/Eigen/src/Eigenvalues/EigenSolver.h b/Eigen/src/Eigenvalues/EigenSolver.h
index b3594655a..bd45d76ac 100644
--- a/Eigen/src/Eigenvalues/EigenSolver.h
+++ b/Eigen/src/Eigenvalues/EigenSolver.h
@@ -343,6 +343,7 @@ typename EigenSolver<MatrixType>::EigenvectorsType EigenSolver<MatrixType>::eige
     {
       // we have a real eigen value
       matV.col(j) = m_eivec.col(j).template cast<ComplexScalar>();
+      matV.col(j).normalize();
     }
     else
     {
diff --git a/test/eigensolver_generic.cpp b/test/eigensolver_generic.cpp
index 26bea9b44..8476f026d 100644
--- a/test/eigensolver_generic.cpp
+++ b/test/eigensolver_generic.cpp
@@ -61,6 +61,7 @@ template<typename MatrixType> void eigensolver(const MatrixType& m)
   VERIFY_IS_APPROX(a * ei1.pseudoEigenvectors(), ei1.pseudoEigenvectors() * ei1.pseudoEigenvalueMatrix());
   VERIFY_IS_APPROX(a.template cast<Complex>() * ei1.eigenvectors(),
                    ei1.eigenvectors() * ei1.eigenvalues().asDiagonal());
+  VERIFY_IS_APPROX(ei1.eigenvectors().colwise().norm(), RealVectorType::Ones(rows).transpose());
   VERIFY_IS_APPROX(a.eigenvalues(), ei1.eigenvalues());
 
   EigenSolver<MatrixType> eiNoEivecs(a, false);