diff --git a/diffdrr/_modidx.py b/diffdrr/_modidx.py
index db423cd6..97b7b223 100644
--- a/diffdrr/_modidx.py
+++ b/diffdrr/_modidx.py
@@ -87,6 +87,8 @@
                               'diffdrr.pose.RigidTransform.__getitem__': ('api/pose.html#rigidtransform.__getitem__', 'diffdrr/pose.py'),
                               'diffdrr.pose.RigidTransform.__init__': ('api/pose.html#rigidtransform.__init__', 'diffdrr/pose.py'),
                               'diffdrr.pose.RigidTransform.__len__': ('api/pose.html#rigidtransform.__len__', 'diffdrr/pose.py'),
+                              'diffdrr.pose.RigidTransform.__matmul__': ('api/pose.html#rigidtransform.__matmul__', 'diffdrr/pose.py'),
+                              'diffdrr.pose.RigidTransform.__new__': ('api/pose.html#rigidtransform.__new__', 'diffdrr/pose.py'),
                               'diffdrr.pose.RigidTransform.compose': ('api/pose.html#rigidtransform.compose', 'diffdrr/pose.py'),
                               'diffdrr.pose.RigidTransform.convert': ('api/pose.html#rigidtransform.convert', 'diffdrr/pose.py'),
                               'diffdrr.pose.RigidTransform.forward': ('api/pose.html#rigidtransform.forward', 'diffdrr/pose.py'),
diff --git a/diffdrr/pose.py b/diffdrr/pose.py
index f8096417..92c9dcb2 100644
--- a/diffdrr/pose.py
+++ b/diffdrr/pose.py
@@ -18,7 +18,15 @@ class RigidTransform(torch.nn.Module):
     inversion, and conversions to various representations of SE(3).
     """
 
+    def __new__(cls, matrix, eps=1e-6):
+        if isinstance(matrix, cls):
+            return matrix
+        return super().__new__(cls)
+
     def __init__(self, matrix, eps=1e-6):
+        if isinstance(matrix, type(self)):
+            return
+
         super().__init__()
         if matrix.dim() == 2:
             matrix = matrix.unsqueeze(0)
@@ -29,7 +37,10 @@ def __len__(self):
         return len(self.matrix)
 
     def __getitem__(self, idx):
-        return self.matrix[idx]
+        return type(self)(self.matrix[idx])
+
+    def __matmul__(self, T):
+        return T.compose(self)
 
     def forward(self, x):
         """Apply (a batch) of rigid transforms to a pointcloud."""
@@ -53,11 +64,11 @@ def inverse(self):
             matrix = make_matrix(Rinv, tinv)
         else:
             matrix = self.matrix.inverse()
-        return RigidTransform(matrix)
+        return type(self)(matrix)
 
     def compose(self, T):
         matrix = torch.einsum("bij, bjk -> bik", T.matrix, self.matrix)
-        return RigidTransform(matrix)
+        return type(self)(matrix)
 
     def convert(self, parameterization, convention=None, degrees=False):
         translation = -self.inverse().translation
diff --git a/notebooks/api/06_pose.ipynb b/notebooks/api/06_pose.ipynb
index b565ea2e..8555a35e 100644
--- a/notebooks/api/06_pose.ipynb
+++ b/notebooks/api/06_pose.ipynb
@@ -102,7 +102,15 @@
     "    inversion, and conversions to various representations of SE(3).\n",
     "    \"\"\"\n",
     "\n",
+    "    def __new__(cls, matrix, eps=1e-6):\n",
+    "        if isinstance(matrix, cls):\n",
+    "            return matrix\n",
+    "        return super().__new__(cls)\n",
+    "\n",
     "    def __init__(self, matrix, eps=1e-6):\n",
+    "        if isinstance(matrix, type(self)):\n",
+    "            return \n",
+    "\n",
     "        super().__init__()\n",
     "        if matrix.dim() == 2:\n",
     "            matrix = matrix.unsqueeze(0)\n",
@@ -113,7 +121,10 @@
     "        return len(self.matrix)\n",
     "\n",
     "    def __getitem__(self, idx):\n",
-    "        return self.matrix[idx]\n",
+    "        return type(self)(self.matrix[idx])\n",
+    "\n",
+    "    def __matmul__(self, T):\n",
+    "        return T.compose(self)\n",
     "\n",
     "    def forward(self, x):\n",
     "        \"\"\"Apply (a batch) of rigid transforms to a pointcloud.\"\"\"\n",
@@ -137,11 +148,11 @@
     "            matrix = make_matrix(Rinv, tinv)\n",
     "        else:\n",
     "            matrix = self.matrix.inverse()\n",
-    "        return RigidTransform(matrix)\n",
+    "        return type(self)(matrix)\n",
     "\n",
     "    def compose(self, T):\n",
     "        matrix = torch.einsum(\"bij, bjk -> bik\", T.matrix, self.matrix)\n",
-    "        return RigidTransform(matrix)\n",
+    "        return type(self)(matrix)\n",
     "\n",
     "    def convert(self, parameterization, convention=None, degrees=False):\n",
     "        translation = -self.inverse().translation\n",