Explain dimension-order alignment with a transposed array

fundamentals/02.3_aligning_data_objects.ipynb

@@ -245,6 +245,36 @@
     "For more, see the [Xarray documentation](https://docs.xarray.dev/en/stable/user-guide/computation.html#broadcasting-by-dimension-name) and the [numpy documentation](https://numpy.org/doc/stable/user/basics.broadcasting.html) on broadcasting.\n"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Dimension order\n",
+    "\n",
+    "Dimensions are matched by name even when they appear in a different order. Transposing `arr1` changes its shape from `(3, 4)` to `(4, 3)`, but each value still has the same `space` and `time` labels. Subtracting the transposed array therefore gives zero at every location, without reshaping either input."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "transposed = arr1.transpose(\"time\", \"space\")\n",
+    "print(arr1.dims, arr1.shape)\n",
+    "print(transposed.dims, transposed.shape)\n",
+    "difference = arr1 - transposed\n",
+    "xr.testing.assert_identical(difference, xr.zeros_like(arr1))\n",
+    "difference"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The values align by name, but the result still has an ordered set of dimensions: dimensions appear in the order they first occur in the inputs. Here `difference.dims` is `('space', 'time')`. Use `.transpose(...)` when you need a particular axis order, especially before passing `.data` to NumPy or another positional array API."
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {