diff --git a/array_api_tests/hypothesis_helpers.py b/array_api_tests/hypothesis_helpers.py
index 7e8780ae..e870a61c 100644
--- a/array_api_tests/hypothesis_helpers.py
+++ b/array_api_tests/hypothesis_helpers.py
@@ -331,11 +331,14 @@ def matrix_shapes(draw, stack_shapes=shapes()):
 square_matrix_shapes = matrix_shapes().filter(lambda shape: shape[-1] == shape[-2])
 
 @composite
-def finite_matrices(draw, shape=matrix_shapes()):
-    return draw(arrays(dtype=floating_dtypes,
-                           shape=shape,
-                           elements=dict(allow_nan=False,
-                                         allow_infinity=False)))
+def finite_matrices(draw, shape=matrix_shapes(), dtype=floating_dtypes, bound=None):
+    # for now, only generate elements from (1, bound); cf symmetric_matrices
+    elements = dict(allow_nan=False, allow_infinity=False)
+    if bound is not None:
+        elements.update(**dict(min_value=1, max_value=bound))
+
+    return draw(arrays(dtype=dtype, shape=shape, elements=elements))
+
 
 rtol_shared_matrix_shapes = shared(matrix_shapes())
 # Should we set a max_value here?
diff --git a/array_api_tests/test_linalg.py b/array_api_tests/test_linalg.py
index 61ec8e0e..9fbee39e 100644
--- a/array_api_tests/test_linalg.py
+++ b/array_api_tests/test_linalg.py
@@ -335,7 +335,7 @@ def test_eigvalsh(x):
 @pytest.mark.unvectorized
 @pytest.mark.xp_extension('linalg')
 @pytest.mark.min_version("2025.12")
-@given(x=arrays(dtype=all_floating_dtypes(), shape=square_matrix_shapes))
+@given(x=finite_matrices(dtype=all_floating_dtypes(), shape=square_matrix_shapes, bound=10))
 def test_eig(x):
     res = linalg.eig(x)
 
@@ -370,7 +370,7 @@ def test_eig(x):
 @pytest.mark.unvectorized
 @pytest.mark.xp_extension('linalg')
 @pytest.mark.min_version("2025.12")
-@given(x=arrays(dtype=all_floating_dtypes(), shape=square_matrix_shapes))
+@given(x=finite_matrices(dtype=all_floating_dtypes(), shape=square_matrix_shapes, bound=10))
 def test_eigvals(x):
     res = linalg.eigvals(x)
     expected_dtype = dh.complex_dtype_for(x.dtype)