diff --git a/test/test_autograd.py b/test/test_autograd.py
index 91da9e79b88..d5dc874812a 100644
--- a/test/test_autograd.py
+++ b/test/test_autograd.py
@@ -2509,9 +2509,7 @@ class TestAutograd(TestCase):
             root = root + torch.eye(dims[-1])
 
             gradcheck(func, [root, upper])
-            # TODO: gradgradcheck does not work correctly yet for complex
-            if not dtype.is_complex:
-                gradgradcheck(func, [root, upper])
+            gradgradcheck(func, [root, upper])
 
             root = torch.rand(*dims, dtype=dtype)
             root = torch.matmul(root, root.transpose(-1, -2).conj())
@@ -2684,9 +2682,9 @@ class TestAutograd(TestCase):
 
     @skipIfNoLapack
     def test_triangular_solve(self):
-        def _test_with_size(A_dims, B_dims):
-            A = torch.rand(*A_dims).requires_grad_()
-            b = torch.rand(*B_dims).requires_grad_()
+        def run_test(A_dims, B_dims, dtype):
+            A = torch.rand(*A_dims, dtype=dtype).requires_grad_()
+            b = torch.rand(*B_dims, dtype=dtype).requires_grad_()
 
             for upper, transpose, unitriangular in product((True, False), repeat=3):
                 def func(A, b):
@@ -2695,10 +2693,11 @@ class TestAutograd(TestCase):
                 gradcheck(func, [A, b])
                 gradgradcheck(func, [A, b])
 
-        _test_with_size((3, 3), (3, 4))
-        _test_with_size((3, 3), (3, 2))
-        _test_with_size((2, 3, 3), (2, 3, 4))
-        _test_with_size((2, 3, 3), (2, 3, 2))
+        for dtype in (torch.double, torch.cdouble):
+            run_test((3, 3), (3, 4), dtype)
+            run_test((3, 3), (3, 2), dtype)
+            run_test((2, 3, 3), (2, 3, 4), dtype)
+            run_test((2, 3, 3), (2, 3, 2), dtype)
 
     @unittest.skipIf(not TEST_MKL, "PyTorch is built without MKL support")
     def test_fft_ifft_rfft_irfft(self):
@@ -4833,7 +4832,11 @@ complex_list = ['t', 'view', 'reshape', 'reshape_as', 'view_as', 'roll', 'clone'
                 'permute', 'squeeze', 'unsqueeze', 'resize', 'resize_as', 'tril', 'triu',
                 'chunk', 'split', 'split_with_sizes', 'repeat', 'expand', 'zero_',
                 'eq_', 'ne_', 'add', '__radd__', 'sum', 'conj', 'sin', 'cos', 'mul', 'sinh',
-                'cosh', '__rmul__', 'sgn', 'abs', 'dot', 'vdot', 'tensor_split'] + separate_complex_tests
+                'cosh', '__rmul__', 'sgn', 'abs', 'dot', 'vdot', 'tensor_split',
+                'matmul', 'bmm', 'mv', 'ger', 'diagonal', ] + separate_complex_tests
+
+# this list corresponds to cases that are not currently implemented
+skip_cuda_list = ['bmm_complex', 'matmul_4d_4d_complex']
 
 # TODO(@anjali411): add tests for 'sub', 'div
 # TODO(@anjali411): add the commented tests back after updating the formula based on tensorflow definition - @anjali411
@@ -5019,6 +5022,11 @@ def add_test(
             for skip in skipTestIf:
                 do_test = skip(do_test)
 
+            # TODO: remove this once tests from skip_cuda_list work
+            do_test = skipCUDAIf(
+                any(skip_test in test_name for skip_test in skip_cuda_list),
+                "not implemented for CUDA yet")(do_test)
+
             setattr(TestAutogradDeviceType, test_name, do_test)
 
 class TestAutogradComplex(TestCase):
diff --git a/tools/autograd/derivatives.yaml b/tools/autograd/derivatives.yaml
index 9c6cd4c578d..eddc30a8604 100644
--- a/tools/autograd/derivatives.yaml
+++ b/tools/autograd/derivatives.yaml
@@ -275,8 +275,8 @@
   self: zeros_like(grad)
 
 - name: bmm(Tensor self, Tensor mat2) -> Tensor
-  self: grad.bmm(mat2.transpose(1, 2))
-  mat2: self.transpose(1, 2).bmm(grad)
+  self: grad.bmm(mat2.transpose(1, 2).conj())
+  mat2: self.transpose(1, 2).conj().bmm(grad)
 
 - name: _bmm(Tensor self, Tensor mat2, *, bool deterministic=False) -> Tensor
   self: at::_bmm(grad, mat2.transpose(1, 2), deterministic)
@@ -498,8 +498,8 @@
   self: not_implemented("geqrf")
 
 - name: ger(Tensor self, Tensor vec2) -> Tensor
-  self: grad.mv(vec2)
-  vec2: grad.t().mv(self)
+  self: grad.mv(vec2.conj())
+  vec2: grad.t().mv(self.conj())
 
 - name: indices(Tensor(a) self) -> Tensor(a)
   output_differentiability: [False]
@@ -749,8 +749,8 @@
   self: mul_tensor_backward(grad, at::scalar_to_tensor(other), self.scalar_type())
 
 - name: mv(Tensor self, Tensor vec) -> Tensor
-  self: grad.ger(vec)
-  vec: self.t().mv(grad)
+  self: grad.ger(vec.conj())
+  vec: self.conj().t().mv(grad)
 
 - name: mvlgamma(Tensor self, int p) -> Tensor
   self: mvlgamma_backward(grad, self, p)
diff --git a/tools/autograd/gen_variable_type.py b/tools/autograd/gen_variable_type.py
index 72fac453413..3cbd585a09c 100644
--- a/tools/autograd/gen_variable_type.py
+++ b/tools/autograd/gen_variable_type.py
@@ -164,7 +164,8 @@ GRADIENT_IMPLEMENTED_FOR_COMPLEX = {
     'cosh', '__rmul__', 'sgn', 'asin', 'acos', 'sub', 'div', 'cat', 'view_as_complex',
     'neg', 'complex', 'select', '_s_where', 'as_strided', 'slice', 'constant_pad_nd',
     'unbind', 'split', 'split_with_sizes', 'unsafe_split', 'split_with_sizes_backward',
-    'dot', 'vdot', 'cholesky'
+    'dot', 'vdot', 'cholesky', 'triangular_solve', 'mm', '_unsafe_view', 'mv', 'ger',
+    'bmm', 'diagonal'
 }
 
 # Some operators invalidate the grad_accumulator. Let's reset it.
diff --git a/torch/csrc/autograd/FunctionsManual.cpp b/torch/csrc/autograd/FunctionsManual.cpp
index 1314a98e956..f807e2b1dff 100644
--- a/torch/csrc/autograd/FunctionsManual.cpp
+++ b/torch/csrc/autograd/FunctionsManual.cpp
@@ -530,9 +530,9 @@ Tensor mm_mat1_backward(const Tensor & grad, const Tensor & mat2, const Tensor &
   at::IntArrayRef sizes = mat1.sizes();
   at::IntArrayRef strides = mat1.strides();
   if (strides[0] == 1 && strides[1] == sizes[0]) {
-    return maybe_multiply(mat2.mm(grad.t()).t(), alpha);
+    return maybe_multiply(mat2.conj().mm(grad.t()).t(), alpha);
   } else {
-    return maybe_multiply(grad.mm(mat2.t()), alpha);
+    return maybe_multiply(grad.mm(mat2.t().conj()), alpha);
   }
 }
 
@@ -550,9 +550,9 @@ Tensor mm_mat2_backward(const Tensor & grad, const Tensor & mat1, IntArrayRef si
       at::addmm_out(r, t, mat1.t(), grad, alpha, 1);
       return r;
     }
-    return maybe_multiply(grad.t().mm(mat1).t(), alpha);
+    return maybe_multiply(grad.t().mm(mat1.conj()).t(), alpha);
   } else {
-    return maybe_multiply(mat1.t().mm(grad), alpha);
+    return maybe_multiply(mat1.t().conj().mm(grad), alpha);
   }
 }
 
@@ -2123,9 +2123,9 @@ std::tuple<Tensor, Tensor> triangular_solve_backward(
   Tensor grad_b, grad_a;
   if (grad_x.defined() || grad_m.defined()) {
     if (grad_x.defined()) {
-      grad_b = std::get<0>(grad_x.triangular_solve(a, upper, !transpose, unitriangular));
+      grad_b = std::get<0>(grad_x.triangular_solve(a.conj(), upper, !transpose, unitriangular));
       if (output_mask[1]) {
-        grad_a = transpose ? -x.matmul(grad_b.transpose(-1, -2)) : -grad_b.matmul(x.transpose(-1, -2));
+        grad_a = transpose ? -x.conj().matmul(grad_b.transpose(-1, -2)) : -grad_b.matmul(x.transpose(-1, -2).conj());
         if (upper) {
           grad_a = grad_a.triu((int) unitriangular);
         } else {