  Normalized eigenvalue counting measure of the sum of two Hermitian (or real
symmetric) matrices $A_{n}$ and $B_{n}$ rotated independently with respect to
each other by the random unitary (or orthogonal) Haar distributed matrix
$U_{n}$ (i.e. $A_{n}+U_{n}^{\ast}B_{n}U_{n}$) is studied in the limit of large
matrix order $n$. Convergence in probability to a limiting nonrandom measure is
established. A functional equation for the Stieltjes transform of the limiting
measure in terms of limiting eigenvalue measures of $A_{n}$ and $B_{n}$ is
obtained and studied.
  Keywords: random matrices, eigenvalue distribution
