The basic operation to be performed is given by 
.
, x and y distributed like vectors:
For this case,
assume that x and y are identically distributed according to
the inducing vector distribution that induced the distribution of matrix A .
Notice that by spreading vectors x and y within columns
and rows of nodes, respectively, we duplicate
all necessary elements of x and y so that local rank-1 updates can
commence on each node.
, other cases:
The case where x and y start as row or column of a matrix
can be derived similar to the special cases of matrix-vector multiplication.