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diff --git a/test/determinant.cpp b/test/determinant.cpp
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+++ b/test/determinant.cpp
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+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#include "main.h"
+
+#include <Eigen/LU>
+
+namespace Eigen {
+
+template<typename MatrixType> void nullDeterminant(const MatrixType& m)
+{
+  /* this test covers the following files:
+     Determinant.h
+  */
+  int rows = m.rows();
+  int cols = m.cols();
+
+  typedef typename MatrixType::Scalar Scalar;
+  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> SquareMatrixType;
+  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
+
+  MatrixType d(rows, cols);
+
+  // build a ill-conditionned matrix with a nul determinant
+  d.col(0).setOnes();
+  d.block(0,1, rows, cols-2).setRandom();
+  d.col(cols-1).setOnes();
+
+  for (int i=0 ; i<rows ; ++i)
+    d.row(i).block(0,1,1,cols-2) = d.row(i).block(0,1,1,cols-2).normalized();
+
+  SquareMatrixType covarianceMatrix = d.transpose() * d;
+
+//   std::cout << covarianceMatrix << "\n" << covarianceMatrix.determinant() << "\n";
+
+  VERIFY_IS_APPROX(covarianceMatrix.determinant(), Scalar(0));
+}
+
+void EigenTest::testDeterminant()
+{
+  for(int i = 0; i < m_repeat; i++) {
+    nullDeterminant(Matrix<float, 30, 3>());
+    nullDeterminant(Matrix<double, 30, 3>());
+    nullDeterminant(Matrix<float, 20, 4>());
+    nullDeterminant(Matrix<double, 20, 4>());
+//     nullDeterminant(MatrixXd(20,4));
+  }
+}
+
+} // namespace Eigen