diff --git a/mlir/include/mlir/Analysis/Presburger/Matrix.h b/mlir/include/mlir/Analysis/Presburger/Matrix.h
--- a/mlir/include/mlir/Analysis/Presburger/Matrix.h
+++ b/mlir/include/mlir/Analysis/Presburger/Matrix.h
@@ -116,8 +116,14 @@
   void negateColumn(unsigned column);
 
   /// Resize the matrix to the specified dimensions. If a dimension is smaller,
-  /// the values are truncated; if it is bigger, the new values are default
-  /// initialized.
+  /// the values are truncated; if it is bigger, the new values are initialized
+  /// to zero.
+  ///
+  /// Due to the representation of the matrix, resizing vertically (adding rows)
+  /// is less expensive than increasing the number of columns beyond
+  /// nReservedColumns.
+  void resize(unsigned newNRows, unsigned newNColumns);
+  void resizeHorizontally(unsigned newNColumns);
   void resizeVertically(unsigned newNRows);
 
   /// Add an extra row at the bottom of the matrix and return its position.
diff --git a/mlir/lib/Analysis/Presburger/Matrix.cpp b/mlir/lib/Analysis/Presburger/Matrix.cpp
--- a/mlir/lib/Analysis/Presburger/Matrix.cpp
+++ b/mlir/lib/Analysis/Presburger/Matrix.cpp
@@ -65,6 +65,18 @@
   return nRows - 1;
 }
 
+void Matrix::resizeHorizontally(unsigned newNColumns) {
+  if (newNColumns < nColumns)
+    removeColumns(newNColumns, nColumns - newNColumns);
+  if (newNColumns > nColumns)
+    insertColumns(nColumns, newNColumns - nColumns);
+}
+
+void Matrix::resize(unsigned newNRows, unsigned newNColumns) {
+  resizeHorizontally(newNColumns);
+  resizeVertically(newNRows);
+}
+
 void Matrix::resizeVertically(unsigned newNRows) {
   nRows = newNRows;
   data.resize(nRows * nReservedColumns);
diff --git a/mlir/unittests/Analysis/Presburger/MatrixTest.cpp b/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
--- a/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
+++ b/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
@@ -166,4 +166,29 @@
       EXPECT_EQ(mat(row, col), row == 5 ? 0 : 10 * row + col);
 }
 
+TEST(MatrixTest, resize) {
+  Matrix mat(5, 5);
+  EXPECT_EQ(mat.getNumRows(), 5u);
+  EXPECT_EQ(mat.getNumColumns(), 5u);
+  for (unsigned row = 0; row < 5; ++row)
+    for (unsigned col = 0; col < 5; ++col)
+      mat(row, col) = 10 * row + col;
+
+  mat.resize(3, 3);
+  ASSERT_TRUE(mat.hasConsistentState());
+  EXPECT_EQ(mat.getNumRows(), 3u);
+  EXPECT_EQ(mat.getNumColumns(), 3u);
+  for (unsigned row = 0; row < 3; ++row)
+    for (unsigned col = 0; col < 3; ++col)
+      EXPECT_EQ(mat(row, col), int(10 * row + col));
+
+  mat.resize(7, 7);
+  ASSERT_TRUE(mat.hasConsistentState());
+  EXPECT_EQ(mat.getNumRows(), 7u);
+  EXPECT_EQ(mat.getNumColumns(), 7u);
+  for (unsigned row = 0; row < 7; ++row)
+    for (unsigned col = 0; col < 7; ++col)
+      EXPECT_EQ(mat(row, col), row >= 3 || col >= 3 ? 0 : int(10 * row + col));
+}
+
 } // namespace mlir