diff --git a/dpctl/tests/test_usm_ndarray_linalg.py b/dpctl/tests/test_usm_ndarray_linalg.py
index 3395bc5026..7d7ba15a50 100644
--- a/dpctl/tests/test_usm_ndarray_linalg.py
+++ b/dpctl/tests/test_usm_ndarray_linalg.py
@@ -783,6 +783,17 @@ def test_tensordot_axes_errors():
         dpt.tensordot(m1, m2, axes=-1)
 
 
+# tests for gh-1570
+def test_tensordot_gemm_small_k_m():
+    get_queue_or_skip()
+
+    x1 = dpt.asarray(1, dtype="i2")
+    x2 = dpt.asarray([0, 1, 0, 0], dtype="i2")
+
+    res = dpt.tensordot(x1, x2, axes=0)
+    assert dpt.all(x2 == res)
+
+
 @pytest.mark.parametrize("dtype", _numeric_types)
 def test_vecdot_1d(dtype):
     q = get_queue_or_skip()
@@ -943,3 +954,29 @@ def test_vecdot_type_promotion(dt1, dt2):
     assert r.shape == tuple()
     assert r.dtype == mul.dtype
     assert dpt.allclose(r, dpt.sum(mul, dtype=mul.dtype))
+
+
+def test_vecdot_broadcast_o1_buffer():
+    get_queue_or_skip()
+
+    v1 = dpt.arange(10, dtype="i2")
+    v2 = dpt.ones((5, 10), dtype="i4")
+
+    res1 = dpt.vecdot(v1, v2)
+    assert res1.shape == (5,)
+
+    res2 = dpt.vecdot(v2, v1)
+    assert res2.shape == (5,)
+
+
+def test_vecdot_contig_small():
+    get_queue_or_skip()
+
+    n = 1
+    for dt in [dpt.int16, dpt.int32, dpt.complex64]:
+        v1 = dpt.zeros((10, n), dtype=dt)
+        v2 = dpt.ones_like(v1, dtype=dt)
+        v1[-1] = 1
+        res = dpt.vecdot(v1, v2)
+        assert dpt.all(res[:-1] == 0)
+        assert res[-1] == n