We consider the existence of distributional (or L-2) solutions of the matri
x refinement equation
<(Phi)over cap> = P(./2)<(Phi)over cap>(./2),
where P is an r x r matrix with trigonometric polynomial entries.
One of the main results of this paper is that the above matrix refinement e
quation has a compactly supported distributional solution if and only if th
e matrix P(0) has an eigenvalue of the form 2(n), n is an element of Z(+).
A characterization of the existence of L-2-solutions of the above matrix re
finement equation in terms of the mask is also given.
A concept of L-2-weak stability of a (finite) sequence of function vectors
is introduced. In the case when the function vectors are solutions of a mat
rix refinement equation, we characterize this weak stability in terms of th
e mask.