DOC: re-wording based on reviews

Author: tacaswell

tutorials/advanced/transforms_tutorial.py

@@ -13,16 +13,16 @@
 available to you, or create your own (see :mod:`matplotlib.transforms`).  The
 table below summarizes some useful coordinate systems, a description of
 each system, and the transformation object for going from each coordinate
-system to the *display* coordinates.  In the ``Transformation Object`` column,
+system to the *display* coordinates.  In the "Transformation Object" column,
 ``ax`` is a :class:`~matplotlib.axes.Axes` instance, and ``fig`` is a
 :class:`~matplotlib.figure.Figure` instance.
 
 +----------------+-----------------------------------+-----------------------------+
 |Coordinate      |Description                        |Transformation object        |
 |system          |                                   |from system to display       |
 +================+===================================+=============================+
-|"data"          |The coordinate system for the data,|``ax.transData``             |
-|                |controlled by xlim and ylim.       |                             |
+|"data"          |The coordinate system of the data  |``ax.transData``             |
+|                |in the Axes.                       |                             |
 +----------------+-----------------------------------+-----------------------------+
 |"axes"          |The coordinate system of the       |``ax.transAxes``             |
 |                |`~matplotlib.axes.Axes`; (0, 0)    |                             |
@@ -71,16 +71,20 @@
 destination coordinate systems, however the objects referred to in the table
 above are constructed to take inputs in their coordinate system, and transform
 the input to the *display* coordinate system.  That is why the *display*
-coordinate system has ``None`` for the ``Transformation Object`` column -- it
+coordinate system has `None` for the "Transformation Object" column -- it
 already is in *display* coordinates.  The naming and destination conventions
 are an aid to keeping track of the available "standard" coordinate systems and
 transforms.
 
-The transformations also know how to invert themselves, to go from *display*
-back to the native coordinate system.  This is particularly useful when
-processing events from the user interface, which typically occur in display
-space, and you want to know where the mouse click or key-press occurred in your
-*data* coordinate system.
+The transformations also know how to invert themselves (via
+`Transform.inverted`) to generate a transform from output coordinate system
+back to the input coordinate system.  For example, ``ax.transData`` converts
+values in data coordinates to display coordinates and
+``ax.transData.inversed()`` is a :class:``matplotlib.transforms.Transform` that
+goes from display coordinates to data coordinates. This is particularly useful
+when processing events from the user interface, which typically occur in
+display space, and you want to know where the mouse click or key-press occurred
+in your *data* coordinate system.
 
 Note that specifying the position of Artists in *display* coordinates may
 change their relative location if the ``dpi`` or size of the figure changes.