diff --git a/test/matrix/test_matrix.rb b/test/matrix/test_matrix.rb
index e38db70..75f41c2 100644
--- a/test/matrix/test_matrix.rb
+++ b/test/matrix/test_matrix.rb
@@ -371,6 +371,14 @@ class TestMatrix < Test::Unit::TestCase
     assert_equal(Matrix[[1,4],[2,5],[3,6]], @m1.transpose)
   end

+  def test_eigensystem
+    m = Matrix[[1, 2], [3, 4]]
+    v, d, v_inv = m.eigensystem
+    assert(d.diagonal?)
+    assert_equal(v.inv, v_inv)
+    assert_equal((v * d * v_inv).round(5), m)
+  end
+
   def test_row_vectors
     assert_equal([Vector[1,2,3], Vector[4,5,6]], @m1.row_vectors)
   end