diff --git a/docs/source/index.rst b/docs/source/index.rst
index a6f4311562..ba0ca7b458 100644
--- a/docs/source/index.rst
+++ b/docs/source/index.rst
@@ -21,6 +21,7 @@ TGM focuses on Image and tensor warping functions such as:
    :caption: Package Reference
 
    geometric
+   transformations
    pinhole
    conversions
    warping
diff --git a/docs/source/transformations.rst b/docs/source/transformations.rst
new file mode 100644
index 0000000000..1a48949452
--- /dev/null
+++ b/docs/source/transformations.rst
@@ -0,0 +1,6 @@
+Linear Transformations
+----------------------
+
+.. currentmodule:: torchgeometry
+
+.. autofunction:: relative_pose
diff --git a/test/test_transformations.py b/test/test_transformations.py
new file mode 100644
index 0000000000..2941a00eac
--- /dev/null
+++ b/test/test_transformations.py
@@ -0,0 +1,90 @@
+import pytest
+
+import torch
+import torchgeometry as tgm
+from torch.autograd import gradcheck
+
+import utils  # test utilities
+from common import TEST_DEVICES
+
+
+class TestTransformPose:
+
+    def _generate_identity_matrix(self, batch_size, device_type):
+        eye = torch.eye(4).repeat(batch_size, 1, 1)  # Nx4x4
+        return eye.to(torch.device(device_type))
+
+    def _test_identity(self):
+        pose_1 = self.pose_1.clone()
+        pose_2 = self.pose_2.clone()
+        pose_21 = tgm.relative_pose(pose_1, pose_2)
+        assert utils.check_equal_torch(pose_21, torch.eye(4).unsqueeze(0))
+
+    def _test_translation(self):
+        offset = 10.
+        pose_1 = self.pose_1.clone()
+        pose_2 = self.pose_2.clone()
+        pose_2[..., :3, -1:] += offset  # add translation
+
+        # compute relative pose
+        pose_21 = tgm.relative_pose(pose_1, pose_2)
+        assert utils.check_equal_torch(pose_21[..., :3, -1:], offset)
+
+    def _test_rotation(self):
+        pose_1 = self.pose_1.clone()
+        pose_2 = torch.zeros_like(pose_1)  # Rz (90deg)
+        pose_2[..., 0, 1] = -1.0
+        pose_2[..., 1, 0] = 1.0
+        pose_2[..., 2, 2] = 1.0
+        pose_2[..., 3, 3] = 1.0
+
+        # compute relative pose
+        pose_21 = tgm.relative_pose(pose_1, pose_2)
+        assert utils.check_equal_torch(pose_21, pose_2)
+
+    def _test_integration(self):
+        pose_1 = self.pose_1.clone()
+        pose_2 = self.pose_2.clone()
+
+        # apply random rotations and translations
+        batch_size, device = pose_2.shape[0], pose_2.device
+        pose_2[..., :3, :3] = torch.rand(batch_size, 3, 3, device=device)
+        pose_2[..., :3, -1:] = torch.rand(batch_size, 3, 1, device=device)
+
+        pose_21 = tgm.relative_pose(pose_1, pose_2)
+        assert utils.check_equal_torch(
+            torch.matmul(pose_21, pose_1), pose_2)
+
+    @pytest.mark.skip("Converting a tensor to a Python boolean ...")
+    def test_jit(self):
+        pose_1 = self.pose_1.clone()
+        pose_2 = self.pose_2.clone()
+
+        pose_21 = tgm.relative_pose(pose_1, pose_2)
+        pose_21_jit = torch.jit.trace(
+            tgm.relative_pose, (pose_1, pose_2,))(pose_1, pose_2)
+        assert utils.check_equal_torch(pose_21, pose_21_jit)
+
+    def _test_gradcheck(self):
+        pose_1 = self.pose_1.clone()
+        pose_2 = self.pose_2.clone()
+
+        pose_1 = utils.tensor_to_gradcheck_var(pose_1)  # to var
+        pose_2 = utils.tensor_to_gradcheck_var(pose_2)  # to var
+        assert gradcheck(tgm.relative_pose, (pose_1, pose_2,),
+                         raise_exception=True)
+
+    @pytest.mark.parametrize("device_type", TEST_DEVICES)
+    @pytest.mark.parametrize("batch_size", [1, 2, 5])
+    def test_run_all(self, batch_size, device_type):
+        # generate identity matrices
+        self.pose_1 = self._generate_identity_matrix(
+            batch_size, device_type)
+        self.pose_2 = self.pose_1.clone()
+
+        # run tests
+        self._test_identity()
+        self._test_translation()
+        self._test_rotation()
+        self._test_integration()
+        self._test_gradcheck()
diff --git a/torchgeometry/__init__.py b/torchgeometry/__init__.py
index 9126467b8c..645a9da739 100644
--- a/torchgeometry/__init__.py
+++ b/torchgeometry/__init__.py
@@ -4,6 +4,7 @@
 from .conversions import *
 from .utils import *
 from .imgwarp import *
+from .transformations import *
 
 from torchgeometry import image
 from torchgeometry import losses
diff --git a/torchgeometry/transformations.py b/torchgeometry/transformations.py
new file mode 100644
index 0000000000..6c46d9e454
--- /dev/null
+++ b/torchgeometry/transformations.py
@@ -0,0 +1,71 @@
+from typing import Optional
+
+import torch
+
+
+__all__ = [
+    "relative_pose",
+]
+
+
+def relative_pose(pose_1: torch.Tensor, pose_2: torch.Tensor,
+                  eps: Optional[float] = 1e-6) -> torch.Tensor:
+    r"""Function that computes the relative transformation from a reference
+    pose :math:`P_1^{\{W\}} = \begin{bmatrix} R_1 & t_1 \\ \mathbf{0} & 1
+    \end{bmatrix}` to destination :math:`P_2^{\{W\}} = \begin{bmatrix} R_2 &
+    t_2 \\ \mathbf{0} & 1 \end{bmatrix}`.
+
+    The relative transformation is computed as follows:
+
+    .. math::
+
+        P_1^{2} = \begin{bmatrix} R_2 R_1^T & R_1^T (t_2 - t_1) \\ \mathbf{0} &
+        1\end{bmatrix}
+
+    Arguments:
+        pose_1 (torch.Tensor): reference pose tensor of shape
+         :math:`(N, 4, 4)`.
+        pose_2 (torch.Tensor): destination pose tensor of shape
+         :math:`(N, 4, 4)`.
+
+    Shape:
+        - Output: :math:`(N, 4, 4)`
+
+    Returns:
+        torch.Tensor: the relative transformation between the poses.
+
+    Example::
+
+        >>> pose_1 = torch.eye(4).unsqueeze(0)  # 1x4x4
+        >>> pose_2 = torch.eye(4).unsqueeze(0)  # 1x4x4
+        >>> pose_21 = tgm.relative_pose(pose_1, pose_2)  # 1x4x4
+    """
+    if not torch.is_tensor(pose_1):
+        raise TypeError("Input pose_1 type is not a torch.Tensor. Got {}"
+                        .format(type(pose_1)))
+    if not torch.is_tensor(pose_2):
+        raise TypeError("Input pose_2 type is not a torch.Tensor. Got {}"
+                        .format(type(pose_2)))
+    if not (len(pose_1.shape) == 3 and pose_1.shape[-2:] == (4, 4)):
+        raise ValueError("Input must be a of the shape Nx4x4."
+                         " Got {}".format(pose_1.shape, pose_2.shape))
+    if not pose_1.shape == pose_2.shape:
+        raise ValueError("Input pose_1 and pose_2 must be a of the same shape."
+                         " Got {}".format(pose_1.shape, pose_2.shape))
+    # unpack input data
+    r_mat_1 = pose_1[..., :3, :3]  # Nx3x3
+    r_mat_2 = pose_2[..., :3, :3]  # Nx3x3
+    t_vec_1 = pose_1[..., :3, -1:]  # Nx3x1
+    t_vec_2 = pose_2[..., :3, -1:]  # Nx3x1
+
+    # compute relative pose
+    r_mat_1_trans = r_mat_1.transpose(1, 2)
+    r_mat_21 = torch.matmul(r_mat_2, r_mat_1_trans)
+    t_vec_21 = torch.matmul(r_mat_1_trans, t_vec_2 - t_vec_1)
+
+    # pack output data
+    pose_21 = torch.zeros_like(pose_1)
+    pose_21[..., :3, :3] = r_mat_21
+    pose_21[..., :3, -1:] = t_vec_21
+    pose_21[..., -1, -1] += 1.0
+    return pose_21 + eps