diff --git a/cml/matrix/comparison.h b/cml/matrix/comparison.h
new file mode 100644
index 0000000..a35210e
--- /dev/null
+++ b/cml/matrix/comparison.h
@@ -0,0 +1,37 @@
+/* -*- C++ -*- ------------------------------------------------------------
+ @@COPYRIGHT@@
+ *-----------------------------------------------------------------------*/
+/** @file
+ */
+
+#pragma once
+
+#ifndef	cml_matrix_comparison_h
+#define	cml_matrix_comparison_h
+
+#include <cml/matrix/readable_matrix.h>
+
+namespace cml {
+
+/** Returns true if the elements of @c left are all equal to the elements
+ * of @c right.
+ */
+template<class Sub1, class Sub2> bool operator==(
+  const readable_matrix<Sub1>& left, const readable_matrix<Sub2>& right);
+
+/** Returns true if some element of @c left is not equal to the same element
+ * of @c right.
+ */
+template<class Sub1, class Sub2> bool operator!=(
+  const readable_matrix<Sub1>& left, const readable_matrix<Sub2>& right);
+
+} // namespace cml
+
+#define __CML_MATRIX_COMPARISON_TPP
+#include <cml/matrix/comparison.tpp>
+#undef __CML_MATRIX_COMPARISON_TPP
+
+#endif
+
+// -------------------------------------------------------------------------
+// vim:ft=cpp:sw=2
diff --git a/cml/matrix/comparison.tpp b/cml/matrix/comparison.tpp
new file mode 100644
index 0000000..fa1e549
--- /dev/null
+++ b/cml/matrix/comparison.tpp
@@ -0,0 +1,41 @@
+/* -*- C++ -*- ------------------------------------------------------------
+ @@COPYRIGHT@@
+ *-----------------------------------------------------------------------*/
+/** @file
+ */
+
+#ifndef __CML_MATRIX_COMPARISON_TPP
+#error "matrix/comparison.tpp not included correctly"
+#endif
+
+#include <cml/matrix/size_checking.h>
+
+namespace cml {
+
+template<class Sub1, class Sub2> inline bool operator==(
+  const readable_matrix<Sub1>& left, const readable_matrix<Sub2>& right
+  )
+{
+  /* Possibly equal only if the same dimensions: */
+  if(left.size() != right.size()) return false;
+  for(int i = 0; i < left.rows(); i ++) {
+    for(int j = 0; j < left.cols(); j ++) {
+      /**/ if(left(i, j) < right(i, j)) return false;	// Strictly less.
+      else if(right(i, j) < left(i, j)) return false;	// Strictly greater.
+      else continue;				        // Possibly equal.
+    }
+  }
+  return true;
+}
+
+template<class Sub1, class Sub2> inline bool operator!=(
+  const readable_matrix<Sub1>& left, const readable_matrix<Sub2>& right
+  )
+{
+  return !(left == right);
+}
+
+} // namespace cml
+
+// -------------------------------------------------------------------------
+// vim:ft=cpp:sw=2
diff --git a/cml/vector/comparison.tpp b/cml/vector/comparison.tpp
index e5bc3c3..d7dbc17 100644
--- a/cml/vector/comparison.tpp
+++ b/cml/vector/comparison.tpp
@@ -16,39 +16,42 @@ template<class Sub1, class Sub2> inline bool operator<(
   const readable_vector<Sub1>& left, const readable_vector<Sub2>& right
   )
 {
-  cml::check_same_size(left, right);
-  for(int i = 0; i < left.size(); i ++) {
+  int n = std::min(left.size(), right.size());
+  for(int i = 0; i < n; i ++) {
     /**/ if(left[i] < right[i]) return true;	// Strictly less.
-    else if(left[i] > right[i]) return false;	// Strictly greater.
-    else continue;				// Equal.
+    else if(right[i] < left[i]) return false;	// Strictly greater.
+    else continue;				// Possibly equal.
   }
 
-  /* Equal. */
-  return false;
+  /* Equal only if the same length: */
+  return left.size() < right.size();
 }
 
 template<class Sub1, class Sub2> inline bool operator>(
   const readable_vector<Sub1>& left, const readable_vector<Sub2>& right
   )
 {
-  cml::check_same_size(left, right);
-  for(int i = 0; i < left.size(); i ++) {
-    /**/ if(left[i] > right[i]) return true;	// Strictly greater.
-    else if(left[i] < right[i]) return false;	// Strictly less.
-    else continue;				// Equal.
+  int n = std::min(left.size(), right.size());
+  for(int i = 0; i < n; i ++) {
+    /**/ if(left[i] < right[i]) return false;	// Strictly less.
+    else if(right[i] < left[i]) return true;	// Strictly greater.
+    else continue;				// Possibly equal.
   }
 
-  /* Equal. */
-  return false;
+  /* Equal only if the same length: */
+  return left.size() > right.size();
 }
 
 template<class Sub1, class Sub2> inline bool operator==(
   const readable_vector<Sub1>& left, const readable_vector<Sub2>& right
   )
 {
-  cml::check_same_size(left, right);
+  /* Possibly equal only if the same length: */
+  if(left.size() != right.size()) return false;
   for(int i = 0; i < left.size(); i ++) {
-    if(!(left[i] == right[i])) return false;	// Not equal.
+    /**/ if(left[i] < right[i]) return false;	// Strictly less.
+    else if(right[i] < left[i]) return false;	// Strictly greater.
+    else continue;				// Possibly equal.
   }
   return true;
 }
diff --git a/tests/matrix/CMakeLists.txt b/tests/matrix/CMakeLists.txt
index 53fff8a..ccd455e 100644
--- a/tests/matrix/CMakeLists.txt
+++ b/tests/matrix/CMakeLists.txt
@@ -23,6 +23,7 @@ CML_ADD_TEST(rowcol1)
 CML_ADD_TEST(lu1)
 CML_ADD_TEST(determinant1)
 CML_ADD_TEST(matrix_hadamard_product1)
+CML_ADD_TEST(matrix_comparison1)
 
 # --------------------------------------------------------------------------
 # vim:ft=cmake
diff --git a/tests/matrix/matrix_comparison1.cpp b/tests/matrix/matrix_comparison1.cpp
new file mode 100644
index 0000000..a1276ee
--- /dev/null
+++ b/tests/matrix/matrix_comparison1.cpp
@@ -0,0 +1,56 @@
+/* -*- C++ -*- ------------------------------------------------------------
+ @@COPYRIGHT@@
+ *-----------------------------------------------------------------------*/
+/** @file
+ */
+
+// Make sure the main header compiles cleanly:
+#include <cml/matrix/comparison.h>
+
+#include <cml/matrix/fixed.h>
+#include <cml/matrix/types.h>
+
+// For Catch:
+#include <cml/util/matrix_print.h>
+
+/* Testing headers: */
+#include "catch_runner.h"
+
+CATCH_TEST_CASE("equal1")
+{
+  auto M = cml::matrix33d(
+    1.,  2.,  3.,
+    1.,  4.,  9.,
+    1., 16., 25.
+    );
+
+  M.transpose();
+  auto expected = cml::matrix33d(
+    1., 1.,  1.,
+    2., 4., 16.,
+    3., 9., 25.
+    );
+
+  CATCH_CHECK(M == expected);
+}
+
+CATCH_TEST_CASE("not_equal1")
+{
+  auto M = cml::matrix33d(
+    1.,  2.,  3.,
+    1.,  4.,  9.,
+    1., 16., 25.
+    );
+
+  M.transpose();
+  auto expected = cml::matrix33d(
+    1., 1.,  1.,
+    2., 4., 16.,
+    3., 9., 24.
+    );
+
+  CATCH_CHECK(M != expected);
+}
+
+// -------------------------------------------------------------------------
+// vim:ft=cpp:sw=2