We explicitly make a distinction between a row or column
of a matrix and a vector. Whenever a vector exists as a row
or column of a matrix, we will refer to it as a (matrix) row
or (matrix) column.
Whenever a vector is *distributed* like a row or column
of a matrix,
without being part of a matrix, we will refer to it as
a *projected row vector* or *projected column vector*.
If a vector is distributed like a row of a matrix, but a copy exists
within every row of nodes, we will refer to it
as a
*duplicated* (projected) row vector
(projected row vector duplicated to all rows of nodes).
Similarly,
if a vector is distributed like a column of a matrix, but a copy exists
within every column of nodes, we will refer to it
as a
*duplicated* (projected) column vector
(projected column vector duplicated to all columns of nodes).