  A left-unilateral matrix equation is an algebraic equation of the form $$
a_0+a_1 x+a_2 x^2+... +a_n x^n=0 $$ where the coefficients $a_r$ and the
unknown $x$ are square matrices of the same order and all coefficients are on
the left (similarly for a right-unilateral equation). Recently certain
perturbative solutions of unilateral equations and their properties have been
discussed. We present a unified approach based on the generalized Bezout
theorem for matrix polynomials. Two equations discussed in the literature,
their perturbative solutions and the relation between them are described. More
abstractly, the coefficients and the unknown can be taken as elements of an
associative, but possibly noncommutative, algebra.
