182182# > Who or what might be missing from the data?
183183
184184# %% [markdown] id="9D4gLiC3Q7DR"
185- # # From Ideas to Code: Why Python?
185+ # ## From Ideas to Code: Why Python?
186186#
187187# Once we define a learning problem, we need to work with the data directly.
188188#
@@ -1395,7 +1395,14 @@ def plot_matrix_flow_and_morph_gif(
13951395
13961396
13971397# %% [markdown]
1398- # ### Example 1: The Identity Matrix
1398+ # ### Examples
1399+ #
1400+ # Five matrices, from the one that does nothing to one that does everything at once.
1401+ # For each, watch both panels: the flow field tells you *where* space moves, the morphing
1402+ # grid tells you *how* the whole plane is reshaped.
1403+
1404+ # %% [markdown]
1405+ # #### Example 1: The Identity Matrix
13991406#
14001407# The identity matrix leaves every vector unchanged.
14011408#
@@ -1417,7 +1424,7 @@ def plot_matrix_flow_and_morph_gif(
14171424)
14181425
14191426# %% [markdown]
1420- # ### Example 2: Stretching Space
1427+ # #### Example 2: Stretching Space
14211428#
14221429# This matrix stretches the first coordinate and slightly shrinks the second coordinate.
14231430#
@@ -1439,7 +1446,7 @@ def plot_matrix_flow_and_morph_gif(
14391446)
14401447
14411448# %% [markdown]
1442- # ### Example 3: Rotating Space
1449+ # #### Example 3: Rotating Space
14431450#
14441451# A rotation matrix turns every point by the same angle.
14451452#
@@ -1463,7 +1470,7 @@ def plot_matrix_flow_and_morph_gif(
14631470)
14641471
14651472# %% [markdown]
1466- # ### Example 4: Mixing Features with a Shear
1473+ # #### Example 4: Mixing Features with a Shear
14671474#
14681475# This matrix mixes the two coordinates.
14691476#
@@ -1485,7 +1492,7 @@ def plot_matrix_flow_and_morph_gif(
14851492)
14861493
14871494# %% [markdown]
1488- # ### Example 5: A General Transformation
1495+ # #### Example 5: A General Transformation
14891496#
14901497# Now try a matrix that stretches, rotates, and mixes coordinates all at once.
14911498#
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