space allocation for a parallel matrix

[Yixun Liu]

Hi,
I am confusing to the allocation for a parallel matrix in PETSC manual,

"If PETSC DECIDE is not used for the arguments m and n, then the user
must ensure that they are chosen
to be compatible with the vectors. To do this, one first considers the
matrix-vector product y = Ax. The m
that is used in the matrix creation routine MatCreateMPIAIJ() must match
the local size used in the vector
creation routine VecCreateMPI() for y. Likewise, the n used must match
that used as the local size in
VecCreateMPI() for x."

Since the process holds all the columns, why does it only hold part of
vector x? Is it convenient for the matrix vector multiplication?

Thanks.

Yixun