diff --git a/test/determinant.cpp b/test/determinant.cpp
new file mode 100644
index 0000000..758f3af
--- /dev/null
+++ b/test/determinant.cpp
@@ -0,0 +1,67 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// 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 <Eigen/LU>
+
+template<typename MatrixType> void determinant(const MatrixType& m)
+{
+  /* this test covers the following files:
+     Determinant.h
+  */
+  typedef typename MatrixType::Index Index;
+  Index size = m.rows();
+
+  MatrixType m1(size, size), m2(size, size);
+  m1.setRandom();
+  m2.setRandom();
+  typedef typename MatrixType::Scalar Scalar;
+  Scalar x = internal::random<Scalar>();
+  VERIFY_IS_APPROX(MatrixType::Identity(size, size).determinant(), Scalar(1));
+  VERIFY_IS_APPROX((m1*m2).eval().determinant(), m1.determinant() * m2.determinant());
+  if(size==1) return;
+  Index i = internal::random<Index>(0, size-1);
+  Index j;
+  do {
+    j = internal::random<Index>(0, size-1);
+  } while(j==i);
+  m2 = m1;
+  m2.row(i).swap(m2.row(j));
+  VERIFY_IS_APPROX(m2.determinant(), -m1.determinant());
+  m2 = m1;
+  m2.col(i).swap(m2.col(j));
+  VERIFY_IS_APPROX(m2.determinant(), -m1.determinant());
+  VERIFY_IS_APPROX(m2.determinant(), m2.transpose().determinant());
+  VERIFY_IS_APPROX(numext::conj(m2.determinant()), m2.adjoint().determinant());
+  m2 = m1;
+  m2.row(i) += x*m2.row(j);
+  VERIFY_IS_APPROX(m2.determinant(), m1.determinant());
+  m2 = m1;
+  m2.row(i) *= x;
+  VERIFY_IS_APPROX(m2.determinant(), m1.determinant() * x);
+  
+  // check empty matrix
+  VERIFY_IS_APPROX(m2.block(0,0,0,0).determinant(), Scalar(1));
+}
+
+void test_determinant()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    int s = 0;
+    CALL_SUBTEST_1( determinant(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST_2( determinant(Matrix<double, 2, 2>()) );
+    CALL_SUBTEST_3( determinant(Matrix<double, 3, 3>()) );
+    CALL_SUBTEST_4( determinant(Matrix<double, 4, 4>()) );
+    CALL_SUBTEST_5( determinant(Matrix<std::complex<double>, 10, 10>()) );
+    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
+    CALL_SUBTEST_6( determinant(MatrixXd(s, s)) );
+    TEST_SET_BUT_UNUSED_VARIABLE(s)
+  }
+}