  A famous theorem by R. Brauer shows how to modify a single eigenvalue of a
matrix by a rank-one update without changing the remaining eigenvalues. A
generalization of this theorem (due to R. Rado) is used to change a pair of
eigenvalues of a symplectic matrix S in a structure-preserving way to desired
target values. Universal bounds on the relative distance between S and the
newly constructed symplectic matrix S' with modified spectrum are given. The
eigenvalues Segre characteristics of S' are related to those of S and a
statement on the eigenvalue condition numbers of S' is derived. The main
results are extended to matrix pencils.
