diff --git a/test/eigensolver_selfadjoint.cpp b/test/eigensolver_selfadjoint.cpp
new file mode 100644
index 0000000..38689cf
--- /dev/null
+++ b/test/eigensolver_selfadjoint.cpp
@@ -0,0 +1,160 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <limits>
+#include <Eigen/Eigenvalues>
+
+template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)
+{
+  typedef typename MatrixType::Index Index;
+  /* this test covers the following files:
+     EigenSolver.h, SelfAdjointEigenSolver.h (and indirectly: Tridiagonalization.h)
+  */
+  Index rows = m.rows();
+  Index cols = m.cols();
+
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+
+  RealScalar largerEps = 10*test_precision<RealScalar>();
+
+  MatrixType a = MatrixType::Random(rows,cols);
+  MatrixType a1 = MatrixType::Random(rows,cols);
+  MatrixType symmA =  a.adjoint() * a + a1.adjoint() * a1;
+  MatrixType symmC = symmA;
+  
+  // randomly nullify some rows/columns
+  {
+    Index count = 1;//internal::random<Index>(-cols,cols);
+    for(Index k=0; k<count; ++k)
+    {
+      Index i = internal::random<Index>(0,cols-1);
+      symmA.row(i).setZero();
+      symmA.col(i).setZero();
+    }
+  }
+  
+  symmA.template triangularView<StrictlyUpper>().setZero();
+  symmC.template triangularView<StrictlyUpper>().setZero();
+
+  MatrixType b = MatrixType::Random(rows,cols);
+  MatrixType b1 = MatrixType::Random(rows,cols);
+  MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1;
+  symmB.template triangularView<StrictlyUpper>().setZero();
+
+  SelfAdjointEigenSolver<MatrixType> eiSymm(symmA);
+  SelfAdjointEigenSolver<MatrixType> eiDirect;
+  eiDirect.computeDirect(symmA);
+  // generalized eigen pb
+  GeneralizedSelfAdjointEigenSolver<MatrixType> eiSymmGen(symmC, symmB);
+
+  VERIFY_IS_EQUAL(eiSymm.info(), Success);
+  VERIFY((symmA.template selfadjointView<Lower>() * eiSymm.eigenvectors()).isApprox(
+          eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal(), largerEps));
+  VERIFY_IS_APPROX(symmA.template selfadjointView<Lower>().eigenvalues(), eiSymm.eigenvalues());
+  
+  VERIFY_IS_EQUAL(eiDirect.info(), Success);
+  VERIFY((symmA.template selfadjointView<Lower>() * eiDirect.eigenvectors()).isApprox(
+          eiDirect.eigenvectors() * eiDirect.eigenvalues().asDiagonal(), largerEps));
+  VERIFY_IS_APPROX(symmA.template selfadjointView<Lower>().eigenvalues(), eiDirect.eigenvalues());
+
+  SelfAdjointEigenSolver<MatrixType> eiSymmNoEivecs(symmA, false);
+  VERIFY_IS_EQUAL(eiSymmNoEivecs.info(), Success);
+  VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmNoEivecs.eigenvalues());
+  
+  // generalized eigen problem Ax = lBx
+  eiSymmGen.compute(symmC, symmB,Ax_lBx);
+  VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
+  VERIFY((symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors()).isApprox(
+          symmB.template selfadjointView<Lower>() * (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
+
+  // generalized eigen problem BAx = lx
+  eiSymmGen.compute(symmC, symmB,BAx_lx);
+  VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
+  VERIFY((symmB.template selfadjointView<Lower>() * (symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox(
+         (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
+
+  // generalized eigen problem ABx = lx
+  eiSymmGen.compute(symmC, symmB,ABx_lx);
+  VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
+  VERIFY((symmC.template selfadjointView<Lower>() * (symmB.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox(
+         (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
+
+
+  eiSymm.compute(symmC);
+  MatrixType sqrtSymmA = eiSymm.operatorSqrt();
+  VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), sqrtSymmA*sqrtSymmA);
+  VERIFY_IS_APPROX(sqrtSymmA, symmC.template selfadjointView<Lower>()*eiSymm.operatorInverseSqrt());
+
+  MatrixType id = MatrixType::Identity(rows, cols);
+  VERIFY_IS_APPROX(id.template selfadjointView<Lower>().operatorNorm(), RealScalar(1));
+
+  SelfAdjointEigenSolver<MatrixType> eiSymmUninitialized;
+  VERIFY_RAISES_ASSERT(eiSymmUninitialized.info());
+  VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvalues());
+  VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
+  VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
+  VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
+
+  eiSymmUninitialized.compute(symmA, false);
+  VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
+  VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
+  VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
+
+  // test Tridiagonalization's methods
+  Tridiagonalization<MatrixType> tridiag(symmC);
+  // FIXME tridiag.matrixQ().adjoint() does not work
+  VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), tridiag.matrixQ() * tridiag.matrixT().eval() * MatrixType(tridiag.matrixQ()).adjoint());
+  
+  if (rows > 1)
+  {
+    // Test matrix with NaN
+    symmC(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
+    SelfAdjointEigenSolver<MatrixType> eiSymmNaN(symmC);
+    VERIFY_IS_EQUAL(eiSymmNaN.info(), NoConvergence);
+  }
+}
+
+void test_eigensolver_selfadjoint()
+{
+  int s = 0;
+  for(int i = 0; i < g_repeat; i++) {
+    // very important to test 3x3 and 2x2 matrices since we provide special paths for them
+    CALL_SUBTEST_1( selfadjointeigensolver(Matrix2f()) );
+    CALL_SUBTEST_1( selfadjointeigensolver(Matrix2d()) );
+    CALL_SUBTEST_1( selfadjointeigensolver(Matrix3f()) );
+    CALL_SUBTEST_1( selfadjointeigensolver(Matrix3d()) );
+    CALL_SUBTEST_2( selfadjointeigensolver(Matrix4d()) );
+    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
+    CALL_SUBTEST_3( selfadjointeigensolver(MatrixXf(s,s)) );
+    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
+    CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(s,s)) );
+    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
+    CALL_SUBTEST_5( selfadjointeigensolver(MatrixXcd(s,s)) );
+    
+    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
+    CALL_SUBTEST_9( selfadjointeigensolver(Matrix<std::complex<double>,Dynamic,Dynamic,RowMajor>(s,s)) );
+
+    // some trivial but implementation-wise tricky cases
+    CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(1,1)) );
+    CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(2,2)) );
+    CALL_SUBTEST_6( selfadjointeigensolver(Matrix<double,1,1>()) );
+    CALL_SUBTEST_7( selfadjointeigensolver(Matrix<double,2,2>()) );
+  }
+
+  // Test problem size constructors
+  s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
+  CALL_SUBTEST_8(SelfAdjointEigenSolver<MatrixXf> tmp1(s));
+  CALL_SUBTEST_8(Tridiagonalization<MatrixXf> tmp2(s));
+  
+  TEST_SET_BUT_UNUSED_VARIABLE(s)
+}
+