To motivate Chapter 
on data duplication and consolidation,
as well as some of the special linear algebra objects
introduced in Chapter 2,
we
give a brief preview of our basic approach to
redistributing and duplicating vectors, and rows and columns
of matrices. We will explain this in the setting of
PBMD without wrapping, with 
.
Notice that the specific case that is used in later chapters
is included in the discussion by considering 
to
be the permutation that produces the wrapping of uniformly
sized sub-vectors of x and y .