diff --git a/singd/structures/base.py b/singd/structures/base.py
index 6f622c3..0680b0d 100644
--- a/singd/structures/base.py
+++ b/singd/structures/base.py
@@ -9,6 +9,7 @@
 import torch
 import torch.distributed as dist
 from torch import Tensor, zeros
+from torch.linalg import matrix_norm
 
 from singd.structures.utils import diag_add_, supported_eye
 
@@ -343,6 +344,15 @@ def infinity_vector_norm(self) -> Tensor:
         # NOTE `.max` can only be called on tensors with non-zero shape
         return max(t.abs().max() for _, t in self.named_tensors() if t.numel() > 0)
 
+    def frobenius_norm(self) -> Tensor:
+        """Compute the Frobenius norm of the represented matrix.
+
+        Returns:
+            The Frobenius norm of the represented matrix.
+        """
+        self._warn_naive_implementation("frobenius_norm")
+        return matrix_norm(self.to_dense())
+
     ###############################################################################
     #                      Special initialization operations                      #
     ###############################################################################
diff --git a/singd/structures/blockdiagonal.py b/singd/structures/blockdiagonal.py
index 2c81b6c..7fb8f1b 100644
--- a/singd/structures/blockdiagonal.py
+++ b/singd/structures/blockdiagonal.py
@@ -7,6 +7,7 @@
 import torch
 from einops import rearrange
 from torch import Tensor, arange, cat, einsum, zeros
+from torch.linalg import vector_norm
 
 from singd.structures.base import StructuredMatrix
 from singd.structures.utils import lowest_precision, supported_eye
@@ -313,6 +314,16 @@ def diag_add_(self, value: float) -> BlockDiagonalMatrixTemplate:
 
         return self
 
+    def frobenius_norm(self) -> Tensor:
+        """Compute the Frobenius norm of the represented matrix.
+
+        Returns:
+            The Frobenius norm of the represented matrix.
+        """
+        return vector_norm(
+            cat([t.flatten() for _, t in self.named_tensors() if t.numel() > 0])
+        )
+
     ###############################################################################
     #                      Special initialization operations                      #
     ###############################################################################
diff --git a/singd/structures/diagonal.py b/singd/structures/diagonal.py
index 74e31ee..affa493 100644
--- a/singd/structures/diagonal.py
+++ b/singd/structures/diagonal.py
@@ -6,6 +6,7 @@
 
 import torch
 from torch import Tensor, einsum, ones, zeros
+from torch.linalg import vector_norm
 
 from singd.structures.base import StructuredMatrix
 
@@ -179,6 +180,14 @@ def diag_add_(self, value: float) -> DiagonalMatrix:
         self._mat_diag.add_(value)
         return self
 
+    def frobenius_norm(self) -> Tensor:
+        """Compute the Frobenius norm of the represented matrix.
+
+        Returns:
+            The Frobenius norm of the represented matrix.
+        """
+        return vector_norm(self._mat_diag)
+
     ###############################################################################
     #                      Special initialization operations                      #
     ###############################################################################
diff --git a/singd/structures/hierarchical.py b/singd/structures/hierarchical.py
index 95c43a6..5cb8489 100644
--- a/singd/structures/hierarchical.py
+++ b/singd/structures/hierarchical.py
@@ -6,6 +6,7 @@
 
 import torch
 from torch import Tensor, arange, cat, einsum, ones, zeros
+from torch.linalg import vector_norm
 
 from singd.structures.base import StructuredMatrix
 from singd.structures.utils import diag_add_, lowest_precision, supported_eye
@@ -353,6 +354,16 @@ def diag_add_(self, value: float) -> HierarchicalMatrixTemplate:
         diag_add_(self.E, value)
         return self
 
+    def frobenius_norm(self) -> Tensor:
+        """Compute the Frobenius norm of the represented matrix.
+
+        Returns:
+            The Frobenius norm of the represented matrix.
+        """
+        return vector_norm(
+            cat([t.flatten() for _, t in self.named_tensors() if t.numel() > 0])
+        )
+
     ###############################################################################
     #                      Special initialization operations                      #
     ###############################################################################
diff --git a/singd/structures/recursive.py b/singd/structures/recursive.py
index 80e277c..f9d6225 100644
--- a/singd/structures/recursive.py
+++ b/singd/structures/recursive.py
@@ -39,18 +39,47 @@ def register_substructure(self, substructure: StructuredMatrix, name: str) -> No
         setattr(self, name, substructure)
         self._substructure_names.append(name)
 
-    def named_tensors(self) -> Iterator[Tuple[str, Tensor]]:
+    def named_tensors(
+        self, include_substructures: bool = True
+    ) -> Iterator[Tuple[str, Tensor]]:
         """Yield all tensors that represent the matrix and their names.
 
+        Args:
+            include_substructures: If `True`, also include the tensors of the
+                substructures. If `False`, exclude them. Default is `True`.
+
         Yields:
             A tuple of the tensor's name and the tensor itself.
         """
         for name in self._tensor_names:
             yield name, getattr(self, name)
+        if include_substructures:
+            for subname, substructure in self.named_substructures():
+                for name, tensor in substructure.named_tensors():
+                    yield f"{name}.{subname}", tensor
+
+    def named_substructures(self) -> Iterator[Tuple[str, StructuredMatrix]]:
+        """Yield all substructures and their names.
+
+        Yields:
+            A tuple of the substructure's name and the substructure itself.
+        """
         for name in self._substructure_names:
-            substructure = getattr(self, name)
-            for sub_name, tensor in substructure.named_tensors():
-                yield f"{name}.{sub_name}", tensor
+            yield name, getattr(self, name)
+
+    def frobenius_norm(self) -> Tensor:
+        """Compute the Frobenius norm of the represented matrix.
+
+        Returns:
+            The Frobenius norm of the represented matrix.
+        """
+        fro_squared = sum(
+            (t**2).sum() for _, t in self.named_tensors(include_substructures=False)
+        )
+        fro_squared_sub = sum(
+            s.frobenius_norm() ** 2 for _, s in self.named_substructures()
+        )
+        return (fro_squared + fro_squared_sub).sqrt()
 
 
 class RecursiveTopRightMatrixTemplate(RecursiveStructuredMatrix):
diff --git a/singd/structures/triltoeplitz.py b/singd/structures/triltoeplitz.py
index 3e85b5d..dd29863 100644
--- a/singd/structures/triltoeplitz.py
+++ b/singd/structures/triltoeplitz.py
@@ -6,6 +6,7 @@
 
 import torch
 from torch import Tensor, arange, cat, zeros
+from torch.linalg import vector_norm
 from torch.nn.functional import conv1d, pad
 
 from singd.structures.base import StructuredMatrix
@@ -191,6 +192,22 @@ def diag_add_(self, value: float) -> TrilToeplitzMatrix:
         self._lower_diags[0].add_(value)
         return self
 
+    def frobenius_norm(self) -> Tensor:
+        """Compute the Frobenius norm of the represented matrix.
+
+        Returns:
+            The Frobenius norm of the represented matrix.
+        """
+        (dim,) = self._lower_diags.shape
+        multiplicity = arange(
+            dim,
+            0,
+            step=-1,
+            dtype=self._lower_diags.dtype,
+            device=self._lower_diags.device,
+        )
+        return vector_norm(self._lower_diags * multiplicity.sqrt())
+
     ###############################################################################
     #                      Special initialization operations                      #
     ###############################################################################
diff --git a/singd/structures/triutoeplitz.py b/singd/structures/triutoeplitz.py
index 832a12e..1a6205d 100644
--- a/singd/structures/triutoeplitz.py
+++ b/singd/structures/triutoeplitz.py
@@ -6,6 +6,7 @@
 
 import torch
 from torch import Tensor, arange, cat, triu_indices, zeros
+from torch.linalg import vector_norm
 from torch.nn.functional import conv1d, pad
 
 from singd.structures.base import StructuredMatrix
@@ -189,6 +190,22 @@ def diag_add_(self, value: float) -> TriuToeplitzMatrix:
         self._upper_diags[0].add_(value)
         return self
 
+    def frobenius_norm(self) -> Tensor:
+        """Compute the Frobenius norm of the represented matrix.
+
+        Returns:
+            The Frobenius norm of the represented matrix.
+        """
+        (dim,) = self._upper_diags.shape
+        multiplicity = arange(
+            dim,
+            0,
+            step=-1,
+            dtype=self._upper_diags.dtype,
+            device=self._upper_diags.device,
+        )
+        return vector_norm(self._upper_diags * multiplicity.sqrt())
+
     ###############################################################################
     #                      Special initialization operations                      #
     ###############################################################################
diff --git a/test/structures/utils.py b/test/structures/utils.py
index b3c69df..145a738 100644
--- a/test/structures/utils.py
+++ b/test/structures/utils.py
@@ -11,7 +11,7 @@
 from matplotlib import pyplot as plt
 from pytest import mark
 from torch import Tensor, device, manual_seed, rand, zeros
-from torch.linalg import vector_norm
+from torch.linalg import matrix_norm, vector_norm
 
 from singd.structures.base import StructuredMatrix
 from singd.structures.utils import is_half_precision, supported_eye
@@ -585,6 +585,22 @@ def test_infinity_vector_norm(self, dev: device, dtype: torch.dtype):
             structured = self.STRUCTURED_MATRIX_CLS.from_dense(sym_mat)
             report_nonclose(truth, structured.infinity_vector_norm())
 
+    @mark.parametrize("dtype", DTYPES, ids=DTYPE_IDS)
+    @mark.parametrize("dev", DEVICES, ids=DEVICE_IDS)
+    def test_frobenius_norm(self, dev: device, dtype: torch.dtype):
+        """Test Frobenius norm of a structured matrix.
+
+        Args:
+            dev: The device on which to run the test.
+            dtype: The data type of the matrices.
+        """
+        for dim in self.DIMS:
+            manual_seed(0)
+            sym_mat = symmetrize(rand((dim, dim), device=dev, dtype=dtype))
+            truth = matrix_norm(self.project(sym_mat))
+            structured = self.STRUCTURED_MATRIX_CLS.from_dense(sym_mat)
+            report_nonclose(truth, structured.frobenius_norm())
+
     @mark.expensive
     def test_visual(self):
         """Create pictures and animations of the structure.