Let A and B be normal endomorphisms with prescribed eigenvalues define
d on a finite dimensional unitary space. A celebrated theorem of Wiela
ndt states that the eigenvalues of A - B are forced to lie in a certai
n subset of the complex plane. The primary objective of this article i
s to extend Wielandt's result to give information about the joint dist
ribution of the eigenvalues of A - B. The main tool in establishing th
is extension is a result on the compounds of unitary matrices. If U is
an n X n unitary matrix, then Birkhoff's famous result on doubly stoc
hastic matrices is often applied to write the matrix (\u(jk)\2)jk as a
convex combination of permutation matrices. The natural generalizatio
n of this process to the compound of a unitary matrix is known to fail
. Here we show that it succeeds if one considers only a certain restri
cted subset of entries.