  The structured pseudospectra of a matrix A are sets of complex numbers that
are eigenvalues of matrices X which are near to A and have the same entries as
A at a fixed set of places. The sum of multiplicities of the eigenvalues of X
inside each connected component of the structured pseudospectra of A does not
depend on X. This fact is known, but not so much as it should be. For this
reason, we give here an elementary and detailed proof of the result.
