diff --git a/core/src/main/scala/dimwit/tensor/Tensor.scala b/core/src/main/scala/dimwit/tensor/Tensor.scala
index 027dba5..5aa4b60 100644
--- a/core/src/main/scala/dimwit/tensor/Tensor.scala
+++ b/core/src/main/scala/dimwit/tensor/Tensor.scala
@@ -330,9 +330,15 @@ object Tensor2:
   def apply[L1: Label, L2: Label](axisExtent1: AxisExtent[L1], axisExtent2: AxisExtent[L2]): Tensor.DefaultsFactory[Tuple2[L1, L2]] = Tensor.DefaultsFactory(Shape(axisExtent1, axisExtent2))
   def apply[L1: Label, L2: Label, V](axisExtent1: AxisExtent[L1], axisExtent2: AxisExtent[L2], vtype: VType[V]): Tensor.TypedFactory[Tuple2[L1, L2], V] = Tensor.TypedFactory(Shape(axisExtent1, axisExtent2), vtype)
 
-  private def eyeImpl[L: Label, V](dim: AxisExtent[L], vtype: VType[V]): Tensor2[L, Prime[L], V] = Tensor(Jax.jnp.eye(dim.size, dtype = vtype.dtype.jaxType))
-  def eye[L: Label](dim: AxisExtent[L]): Tensor2[L, Prime[L], Float32] = eyeImpl(dim, VType[Float32])
-  def eye[L: Label, V](dim: AxisExtent[L], vtype: VType[V]): Tensor2[L, Prime[L], V] = eyeImpl(dim, vtype)
+  private def eyeImpl[T <: Tuple: Labels, V](n: Int, m: Int, vtype: VType[V] = VType[Float32]): Tensor[T, V] = Tensor(Jax.jnp.eye(n, m, dtype = vtype.dtype.jaxType))
+
+  def eye[L: Label](dim: AxisExtent[L]): Tensor2[L, Prime[L], Float32] = eye(dim, Axis[Prime[L]] -> dim.size)
+  def eye[L: Label, V](dim: AxisExtent[L], vtype: VType[V]): Tensor2[L, Prime[L], V] = eye(dim, Axis[Prime[L]] -> dim.size, vtype)
+  def eye[L1: Label, L2: Label](n: AxisExtent[L1], m: AxisExtent[L2]): Tensor2[L1, L2, Float32] = eyeImpl[(L1, L2), Float32](n.size, m.size)
+  def eye[L1: Label, L2: Label, V](n: AxisExtent[L1], m: AxisExtent[L2], vtype: VType[V]): Tensor2[L1, L2, V] = eyeImpl[(L1, L2), V](n.size, m.size, vtype)
+  def eye[L1: Label, L2: Label](shape: Shape2[L1, L2]): Tensor2[L1, L2, Float32] = eye(shape.extent(Axis[L1]), shape.extent(Axis[L2]))
+  def eye[L1: Label, L2: Label, V](shape: Shape2[L1, L2], vtype: VType[V]): Tensor2[L1, L2, V] = eye(shape.extent(Axis[L1]), shape.extent(Axis[L2]), vtype)
+
   def diag[L: Label, V](diag: Tensor1[L, V]): Tensor2[L, Prime[L], V] = Tensor(Jax.jnp.diag(diag.jaxValue))
 
 /** Companion object for Tensors of rank 3.
diff --git a/core/src/test/scala/dimwit/tensor/TensorCreationSuite.scala b/core/src/test/scala/dimwit/tensor/TensorCreationSuite.scala
index b2023e8..9dccf79 100644
--- a/core/src/test/scala/dimwit/tensor/TensorCreationSuite.scala
+++ b/core/src/test/scala/dimwit/tensor/TensorCreationSuite.scala
@@ -92,3 +92,45 @@ class TensorCreationSuite extends DimwitTest:
         idx(Axis[A]).toFloat
       }
       result shouldEqual Tensor1(Axis[A]).fromArray(Array(0.0f, 1.0f, 2.0f, 3.0f))
+
+  describe("eye"):
+
+    it("square: from a single extent"):
+      val result = Tensor2.eye(Axis[A] -> 3)
+      result.shape shouldEqual Shape2(Axis[A] -> 3, Axis[Prime[A]] -> 3)
+      result shouldEqual Tensor2(Axis[A], Axis[B]).fromArray(
+        Array(Array(1.0f, 0.0f, 0.0f), Array(0.0f, 1.0f, 0.0f), Array(0.0f, 0.0f, 1.0f))
+      )
+
+    it("square: from two extents and from a shape"):
+      val expected = Tensor2(Axis[A], Axis[B]).fromArray(
+        Array(Array(1.0f, 0.0f), Array(0.0f, 1.0f))
+      )
+      Tensor2.eye(Axis[A] -> 2, Axis[B] -> 2) shouldEqual expected
+      Tensor2.eye(Shape2(Axis[A] -> 2, Axis[B] -> 2)) shouldEqual expected
+
+    it("wide: more columns than rows, zero padded"):
+      val expected = Tensor2(Axis[A], Axis[B]).fromArray(
+        Array(Array(1.0f, 0.0f, 0.0f), Array(0.0f, 1.0f, 0.0f))
+      )
+      val fromExtents = Tensor2.eye(Axis[A] -> 2, Axis[B] -> 3)
+      fromExtents.shape shouldEqual Shape2(Axis[A] -> 2, Axis[B] -> 3)
+      fromExtents shouldEqual expected
+      Tensor2.eye(Shape2(Axis[A] -> 2, Axis[B] -> 3)) shouldEqual expected
+
+    it("tall: more rows than columns, truncating"):
+      val expected = Tensor2(Axis[A], Axis[B]).fromArray(
+        Array(Array(1.0f, 0.0f), Array(0.0f, 1.0f), Array(0.0f, 0.0f))
+      )
+      val fromExtents = Tensor2.eye(Axis[A] -> 3, Axis[B] -> 2)
+      fromExtents.shape shouldEqual Shape2(Axis[A] -> 3, Axis[B] -> 2)
+      fromExtents shouldEqual expected
+      Tensor2.eye(Shape2(Axis[A] -> 3, Axis[B] -> 2)) shouldEqual expected
+
+    it("defaults to Float32 and accepts an explicit vtype in all variants"):
+      Tensor2.eye(Axis[A] -> 2).dtype shouldBe DType.Float32
+      Tensor2.eye(Axis[A] -> 2, Axis[B] -> 3).dtype shouldBe DType.Float32
+      Tensor2.eye(Shape2(Axis[A] -> 2, Axis[B] -> 3)).dtype shouldBe DType.Float32
+      Tensor2.eye(Axis[A] -> 2, VType[Int32]).dtype shouldBe DType.Int32
+      Tensor2.eye(Axis[A] -> 2, Axis[B] -> 3, VType[Int32]).dtype shouldBe DType.Int32
+      Tensor2.eye(Shape2(Axis[A] -> 2, Axis[B] -> 3), VType[Int32]).dtype shouldBe DType.Int32