diff --git a/onnxscript/function_libs/torch_aten/ops/core.py b/onnxscript/function_libs/torch_aten/ops/core.py
index 377e25eb86..5dbe60d931 100644
--- a/onnxscript/function_libs/torch_aten/ops/core.py
+++ b/onnxscript/function_libs/torch_aten/ops/core.py
@@ -2680,10 +2680,10 @@ def aten_masked_select_backward(
     raise NotImplementedError()
 
 
-def aten_matmul(self: TensorType, other: TensorType) -> TensorType:
+def aten_matmul(self, other):
     # matmul(Tensor self, Tensor other) -> Tensor
 
-    raise NotImplementedError()
+    return op.MatMul(self, other)
 
 
 def aten_matmul_backward(
@@ -3080,10 +3080,11 @@ def aten_mkldnn_max_pool3d_backward(
     raise NotImplementedError()
 
 
-def aten_mm(self: TensorType, mat2: TensorType) -> TensorType:
+def aten_mm(self, mat2):
     # mm(Tensor self, Tensor mat2) -> Tensor
 
-    raise NotImplementedError()
+    # TODO(justinchuby): Specify type conversion for uint8/int8/int16
+    return op.MatMul(self, mat2)
 
 
 def aten_mode(
@@ -3463,16 +3464,13 @@ def aten_nuclear_norm(self: TensorType, keepdim: bool = False) -> TensorType:
     raise NotImplementedError()
 
 
-def aten_numpy_T(self: TensorType) -> TensorType:
-    # numpy_T(Tensor(a) self) -> Tensor(a)
-
-    raise NotImplementedError()
-
-
-def aten_ones(size: INT64) -> TensorType:
+def aten_ones(size: INT64, dtype: int = -1) -> TensorType:
     # ones(SymInt[] size, *, ScalarType? dtype=None, Layout? layout=None, Device? device=None, bool? pin_memory=None) -> Tensor
 
-    raise NotImplementedError()
+    one = op.Constant(value_float=1)
+    if dtype != -1:
+        one = op.Cast(one, to=dtype)  # type: ignore[arg-type]
+    return op.Expand(one, size)  # type: ignore[arg-type]
 
 
 def aten_ones_like(self, dtype: int = -1):
@@ -4461,7 +4459,13 @@ def aten_symeig(
 def aten_t(self: TensorType) -> TensorType:
     # t(Tensor(a) self) -> Tensor(a)
 
-    raise NotImplementedError()
+    # TODO(justinchuby): Make rank a function
+    rank = op.Size(op.Shape(self))  # type: ignore[arg-type]
+    if rank == 0 or rank == 1:  # pylint: disable=consider-using-in
+        result = self
+    else:
+        result = op.Transpose(self, perm=[1, 0])  # type: ignore[arg-type]
+    return result
 
 
 def aten_t_copy(self: TensorType) -> TensorType:
@@ -4606,6 +4610,13 @@ def aten_trace_backward(grad: TensorType, sizes: INT64) -> TensorType:
     raise NotImplementedError()
 
 
+def aten_transpose(self, dim0: int, dim1: int):
+    # transpose.int(Tensor(a) self, int dim0, int dim1) -> Tensor(a)
+
+    # FIXME(justinchuby): onnxscript raises Unsupported expression type
+    return op.Transpose(self, [dim0, dim1])
+
+
 def aten_triangular_solve(
     self: TensorType,
     A: TensorType,
diff --git a/onnxscript/function_libs/torch_aten/ops/nn.py b/onnxscript/function_libs/torch_aten/ops/nn.py
index a88874183d..d76250ea8a 100644
--- a/onnxscript/function_libs/torch_aten/ops/nn.py
+++ b/onnxscript/function_libs/torch_aten/ops/nn.py
@@ -407,12 +407,21 @@ def aten_leaky_relu_backward(
     raise NotImplementedError()
 
 
-def aten_linear(
-    input: TensorType, weight: TensorType, bias: Optional[TensorType] = None
-) -> TensorType:
+def aten_linear(input, weight, bias=None) -> TensorType:
     # linear(Tensor input, Tensor weight, Tensor? bias=None) -> Tensor
 
-    raise NotImplementedError()
+    # FIXME(justinchuby): Enable the test
+    # INVALID_GRAPH : This is an invalid model.
+    # In Node, ("", OptionalHasElement, "", -1) : () -> ("output0",) ,
+    # Error Node () has input size 0 not in range [min=1, max=1]
+
+    # NOTE: The symbolic function in torch.onnx also uses Gemm in certain cases
+    # Optimizers may consider this path and replace it with Gemm
+    result = op.MatMul(input, weight)
+    if op.OptionalHasElement(bias):
+        bias = op.OptionalGetElement(bias)
+        result = op.Add(result, bias)  # type: ignore[arg-type]
+    return result
 
 
 def aten_log_sigmoid(self: TensorType) -> TensorType:
diff --git a/onnxscript/test/function_libs/torch_aten/ops_correctness_test.py b/onnxscript/test/function_libs/torch_aten/ops_correctness_test.py
index a2a9dbac7c..7c9a67496d 100644
--- a/onnxscript/test/function_libs/torch_aten/ops_correctness_test.py
+++ b/onnxscript/test/function_libs/torch_aten/ops_correctness_test.py
@@ -162,35 +162,56 @@ def wrapped(fn):
 # Find the names of the OpInfos in torch/testing/_internal/common_methods_invocations.py
 OPINFO_FUNCTION_MAPPING: dict[str, Callable[..., Any]] = {
     "add": core_ops.aten_add,
-    # "clamp": core_ops.aten_clamp,  # TODO(justinchuby): Enable
     "clamp_max": core_ops.aten_clamp_max_tensor,
     "clamp_min": core_ops.aten_clamp_min_tensor,
+    "clamp": core_ops.aten_clamp,
     "gt": core_ops.aten_gt,
     "lt": core_ops.aten_lt,
+    "matmul": core_ops.aten_matmul,
+    "mm": core_ops.aten_mm,
     "mul": core_ops.aten_mul,
     "nn.functional.elu": nn_ops.aten_elu,
+    "nn.functional.linear": nn_ops.aten_linear,
     "nn.functional.relu6": nn_ops.aten_relu6,
     "nn.functional.selu": core_ops.aten_selu,
     "ones_like": core_ops.aten_ones_like,
+    "ones": core_ops.aten_ones,
     "repeat": core_ops.aten_repeat,
     "round": core_ops.aten_round,
     "sub": core_ops.aten_sub,
+    "t": core_ops.aten_t,
+    # "transpose": core_ops.aten_transpose,  # TODO(justinchuby): Enable when onnxscript errors are fixed
 }
 
 TESTED_OPS = frozenset(OPINFO_FUNCTION_MAPPING)
 
 EXPECTED_SKIPS_OR_FAILS = (
     xfail("add", dtypes=BOOL_TYPES, reason="Add is not defined on bool tensors"),
+    skip("clamp", reason="Enable when onnxscript errors are fixed"),
     xfail("clamp_max", dtypes=BOOL_TYPES, reason="Min is not defined on bool tensors"),
     xfail("clamp_min", dtypes=BOOL_TYPES, reason="Max is not defined on bool tensors"),
     xfail("gt", dtypes=BOOL_TYPES, reason="Greater is not defined on bool tensors"),
     xfail("lt", dtypes=BOOL_TYPES, reason="Less is not defined on bool tensors"),
+    xfail(
+        "matmul",
+        dtypes=[torch.uint8, torch.int8, torch.int16],
+        reason="MatMul is not defined on int16/int8/uint8 tensors",
+    ),
+    xfail(
+        "mm",
+        dtypes=[torch.uint8, torch.int8, torch.int16],
+        reason="MatMul is not defined on int16/int8/uint8 tensors",
+    ),
     xfail("mul", dtypes=BOOL_TYPES, reason="Mul is not defined on bool tensors"),
     xfail(
         "nn.functional.elu",
         dtypes=dtypes_except(torch.float16, torch.float32),
         reason="ONNX Runtime doesn't support float64 for Elu",
     ),
+    xfail(
+        "nn.functional.linear",
+        reason="ONNX Runtime thinks the graph is invalid",
+    ),
     xfail(
         "nn.functional.relu6",
         dtypes=dtypes_except(torch.float16, torch.float32),
@@ -213,6 +234,7 @@ def wrapped(fn):
         "round", variant_name="decimals_neg_3", reason="The ATen op does not support decimals"
     ),
     xfail("sub", dtypes=BOOL_TYPES, reason="Sub is not defined on bool tensors"),
+    xfail("transpose", reason="Enable when onnxscript errors are fixed"),
 )
 
 
@@ -240,6 +262,10 @@ def wrapped(fn):
 
 OPS_DB = copy.deepcopy(common_methods_invocations.op_db)
 
+ALL_OPS_IN_DB = frozenset(op_info.name for op_info in OPS_DB)
+# Assert all ops in OPINFO_FUNCTION_MAPPING are in the OPS_DB
+assert TESTED_OPS.issubset(ALL_OPS_IN_DB), f"{TESTED_OPS - ALL_OPS_IN_DB} not in OPS_DB"
+
 
 TORCH_TYPE_TO_ONNX = {
     torch.bool: onnx.TensorProto.BOOL,
@@ -369,10 +395,21 @@ def test_output_match(self, device: str, dtype: torch.dtype, op):
                     )
                 # pylint: enable=c-extension-no-member
 
+                if dtype == torch.float32:
+                    # Relax atol and rtol for float32 based on empirical results
+                    # The current most relaxed values are for aten::matmul
+                    rtol = 3.7e-6
+                    atol = 1.8e-5
+                else:
+                    rtol = None
+                    atol = None
+
                 # Use torch testing to ensure dtypes and shapes match
                 torch.testing.assert_close(
                     torch.tensor(function_output),
                     output_torch,
+                    rtol=rtol,
+                    atol=atol,
                 )