diff --git a/pytensor/tensor/nlinalg.py b/pytensor/tensor/nlinalg.py
index dd9b132af4..2ccc1c5930 100644
--- a/pytensor/tensor/nlinalg.py
+++ b/pytensor/tensor/nlinalg.py
@@ -42,7 +42,11 @@ def make_node(self, x):
             out_dtype = "float64"
         else:
             out_dtype = x.dtype
-        return Apply(self, [x], [matrix(shape=x.type.shape, dtype=out_dtype)])
+        return Apply(
+            self,
+            [x],
+            [matrix(shape=(x.type.shape[1], x.type.shape[0]), dtype=out_dtype)],
+        )
 
     def perform(self, node, inputs, outputs):
         (x,) = inputs
diff --git a/tests/tensor/test_nlinalg.py b/tests/tensor/test_nlinalg.py
index 0aea17af7e..a9624fd47d 100644
--- a/tests/tensor/test_nlinalg.py
+++ b/tests/tensor/test_nlinalg.py
@@ -70,6 +70,21 @@ def test_pseudoinverse_grad():
     utt.verify_grad(pinv, [r])
 
 
+def test_pseudoinverse_static_shape():
+    x = matrix(shape=(3, 5))
+    z = pinv(x)
+    assert z.type.shape == (5, 3)
+
+    g = pytensor.grad(z.sum(), x)
+    f = function([x], g)
+
+    rng = np.random.default_rng(utt.fetch_seed())
+    r = rng.standard_normal((3, 5)).astype(config.floatX)
+    assert f(r).shape == (3, 5)
+
+    utt.verify_grad(pinv, [r])
+
+
 class TestMatrixInverse(utt.InferShapeTester):
     def setup_method(self):
         super().setup_method()