Your second idea is definitely better, and it is sufficient, I believe. If you compare the statement

with

Find an s.t.

then why not just solve

for

Dimensions:

is n x n,

is n x m,

is p x n

must be m x n, and so

must be m x p.

As for the restriction, I wouldn't worry about it at all. If an operator takes into then it must, of necessity, take a subset into