diff --git a/Eigen/src/Eigenvalues/ComplexEigenSolver.h b/Eigen/src/Eigenvalues/ComplexEigenSolver.h
index 50fa3b809..c0aae46ff 100644
--- a/Eigen/src/Eigenvalues/ComplexEigenSolver.h
+++ b/Eigen/src/Eigenvalues/ComplexEigenSolver.h
@@ -265,8 +265,6 @@ template <typename MatrixType>
 void ComplexEigenSolver<MatrixType>::doComputeEigenvectors(RealScalar matrixnorm) {
   const Index n = m_eivalues.size();
 
-  matrixnorm = numext::maxi(matrixnorm, (std::numeric_limits<RealScalar>::min)());
-
   // Compute X such that T = X D X^(-1), where D is the diagonal of T.
   // The matrix X is unit triangular.
   m_matX = EigenvectorType::Zero(n, n);
@@ -282,7 +280,8 @@ void ComplexEigenSolver<MatrixType>::doComputeEigenvectors(RealScalar matrixnorm
       if (z == ComplexScalar(0)) {
         // If the i-th and k-th eigenvalue are equal, then z equals 0.
         // Use a small value instead, to prevent division by zero.
-        numext::real_ref(z) = NumTraits<RealScalar>::epsilon() * matrixnorm;
+        numext::real_ref(z) = numext::maxi(std::numeric_limits<RealScalar>::epsilon() * matrixnorm,
+                                           (std::numeric_limits<RealScalar>::min)());
       }
       m_matX.coeffRef(i, k) = m_matX.coeff(i, k) / z;
     }
diff --git a/test/eigensolver_complex.cpp b/test/eigensolver_complex.cpp
index 76846a933..159009260 100644
--- a/test/eigensolver_complex.cpp
+++ b/test/eigensolver_complex.cpp
@@ -132,7 +132,8 @@ void eigensolver(const MatrixType& m) {
     ComplexEigenSolver<MatrixType> ei3(a);
     VERIFY_IS_EQUAL(ei3.info(), Success);
     VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(), RealScalar(1));
-    VERIFY((ei3.eigenvectors().transpose() * ei3.eigenvectors().transpose()).eval().isIdentity());
+    RealScalar tol = 2 * a.cols() * NumTraits<RealScalar>::epsilon();
+    VERIFY((ei3.eigenvectors().adjoint() * ei3.eigenvectors()).eval().isIdentity(tol));
   }
 }
 
diff --git a/test/eigensolver_generic.cpp b/test/eigensolver_generic.cpp
index c665df8d8..dafaf99b3 100644
--- a/test/eigensolver_generic.cpp
+++ b/test/eigensolver_generic.cpp
@@ -89,7 +89,8 @@ void eigensolver(const MatrixType& m) {
     EigenSolver<MatrixType> ei3(a);
     VERIFY_IS_EQUAL(ei3.info(), Success);
     VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(), RealScalar(1));
-    VERIFY((ei3.eigenvectors().transpose() * ei3.eigenvectors().transpose()).eval().isIdentity());
+    RealScalar tol = 2 * a.cols() * NumTraits<RealScalar>::epsilon();
+    VERIFY((ei3.eigenvectors().adjoint() * ei3.eigenvectors()).eval().isIdentity(tol));
   }
 }
 
diff --git a/test/eigensolver_selfadjoint.cpp b/test/eigensolver_selfadjoint.cpp
index 12bc3b1f7..7cc4d636f 100644
--- a/test/eigensolver_selfadjoint.cpp
+++ b/test/eigensolver_selfadjoint.cpp
@@ -197,7 +197,8 @@ void selfadjointeigensolver(const MatrixType& m) {
     SelfAdjointEigenSolver<MatrixType> ei3(a);
     VERIFY_IS_EQUAL(ei3.info(), Success);
     VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(), RealScalar(1));
-    VERIFY((ei3.eigenvectors().transpose() * ei3.eigenvectors().transpose()).eval().isIdentity());
+    RealScalar tol = 2 * a.cols() * NumTraits<RealScalar>::epsilon();
+    VERIFY((ei3.eigenvectors().adjoint() * ei3.eigenvectors()).eval().isIdentity(tol));
   }
 }