--- a/doc/interpreter/vectorize.txi
+++ b/doc/interpreter/vectorize.txi
@@ -621,5 +621,35 @@
 @node Examples
 @section Examples
 
-Here goes a gallery of vectorization puzzles with solutions culled from
-the help mailing list and the machine learning class...
+The following are examples of vectorization questions asked by actual
+users of Octave and their solutions.
+
+@c FIXME: We need a lot more examples here.
+
+@itemize @bullet
+@item
+For a vector @code{A}, the following loop
+
+@example
+@group
+n = length (A);
+B = zeros (n, 2);
+for i = 1:length(A)
+  ## this will be two columns, the first is the difference and
+  ## the second the mean of the two elements used for the diff.
+  B(i,:) = [A(i+1)-A(i), (A(i+1) + A(i))/2)];
+end
+@end group
+@end example
+
+@noindent
+can be turned into the following one-liner:
+
+@example
+B = [diff(A)(:), 0.5*(A(1:end-1)+A(2:end))(:)]
+@end example
+
+Note the usage of colon indexing to flatten an intermediate result into
+a column vector. This is a common vectorization trick.
+
+@end itemize