diff --git a/.github/workflows/array-api-tests-torch.yml b/.github/workflows/array-api-tests-torch.yml
index 3f87ecae..98234ae2 100644
--- a/.github/workflows/array-api-tests-torch.yml
+++ b/.github/workflows/array-api-tests-torch.yml
@@ -10,3 +10,5 @@ jobs:
       # Proper linalg testing will require
       # https://github.com/data-apis/array-api-tests/pull/101
       pytest-extra-args: "--disable-extension linalg"
+      extra-env-vars: |
+        ARRAY_API_TESTS_SKIP_DTYPES=uint16,uint32,uint64
diff --git a/.github/workflows/array-api-tests.yml b/.github/workflows/array-api-tests.yml
index c1c709a7..6e709438 100644
--- a/.github/workflows/array-api-tests.yml
+++ b/.github/workflows/array-api-tests.yml
@@ -27,7 +27,10 @@ on:
       skips-file-extra:
         required: false
         type: string
-
+      extra-env-vars:
+        required: false
+        type: string
+        description: "Multiline string of environment variables to set for the test run."
 
 env:
   PYTEST_ARGS: "--max-examples 200 -v -rxXfE --ci ${{ inputs.pytest-extra-args }} --hypothesis-disable-deadline"
@@ -54,6 +57,11 @@ jobs:
       uses: actions/setup-python@v5
       with:
         python-version: ${{ matrix.python-version }}
+    - name: Set Extra Environment Variables
+      # Set additional environment variables if provided
+      if: inputs.extra-env-vars
+      run: |
+        echo "${{ inputs.extra-env-vars }}" >> $GITHUB_ENV
     - name: Install dependencies
       # NumPy 1.21 doesn't support Python 3.11. There doesn't seem to be a way
       # to put this in the numpy 1.21 config file.
diff --git a/array_api_compat/torch/linalg.py b/array_api_compat/torch/linalg.py
index 7e7e2415..e26198b9 100644
--- a/array_api_compat/torch/linalg.py
+++ b/array_api_compat/torch/linalg.py
@@ -60,6 +60,22 @@ def vecdot(x1: array, x2: array, /, *, axis: int = -1, **kwargs) -> array:
 
 def solve(x1: array, x2: array, /, **kwargs) -> array:
     x1, x2 = _fix_promotion(x1, x2, only_scalar=False)
+    # Torch tries to emulate NumPy 1 solve behavior by using batched 1-D solve
+    # whenever
+    # 1. x1.ndim - 1 == x2.ndim
+    # 2. x1.shape[:-1] == x2.shape
+    #
+    # See linalg_solve_is_vector_rhs in
+    # aten/src/ATen/native/LinearAlgebraUtils.h and
+    # TORCH_META_FUNC(_linalg_solve_ex) in
+    # aten/src/ATen/native/BatchLinearAlgebra.cpp in the PyTorch source code.
+    #
+    # The easiest way to work around this is to prepend a size 1 dimension to
+    # x2, since x2 is already one dimension less than x1.
+    #
+    # See https://github.com/pytorch/pytorch/issues/52915
+    if x2.ndim != 1 and x1.ndim - 1 == x2.ndim and x1.shape[:-1] == x2.shape:
+        x2 = x2[None]
     return torch.linalg.solve(x1, x2, **kwargs)
 
 # torch.trace doesn't support the offset argument and doesn't support stacking
@@ -78,7 +94,23 @@ def vector_norm(
 ) -> array:
     # torch.vector_norm incorrectly treats axis=() the same as axis=None
     if axis == ():
-        keepdims = True
+        out = kwargs.get('out')
+        if out is None:
+            dtype = None
+            if x.dtype == torch.complex64:
+                dtype = torch.float32
+            elif x.dtype == torch.complex128:
+                dtype = torch.float64
+
+            out = torch.zeros_like(x, dtype=dtype)
+
+        # The norm of a single scalar works out to abs(x) in every case except
+        # for ord=0, which is x != 0.
+        if ord == 0:
+            out[:] = (x != 0)
+        else:
+            out[:] = torch.abs(x)
+        return out
     return torch.linalg.vector_norm(x, ord=ord, axis=axis, keepdim=keepdims, **kwargs)
 
 __all__ = linalg_all + ['outer', 'matmul', 'matrix_transpose', 'tensordot',