  Matrix polynomials with unitary/doubly stochastic coefficients form the
subject matter of this manuscript. We prove that if $P(\lambda)$ is a quadratic
matrix polynomial whose coefficients are either unitary matrices or doubly
stochastic matrices, then under certain conditions on these coefficients, the
corresponding block companion matrix $C$ is diagonalizable. Consequently, if
$Q(\lambda)$ is another quadratic matrix polynomial with corresponding block
companion matrix $D$, then a Hoffman-Wielandt type inequality holds for the
block companion matrices $C$ and $D$.
