Representation of solutions to a linear matrix first-order differential equation with delay

Linear matrix delayed differential equation [Formula: see text] is dealt with, where [Formula: see text] is a delay, [Formula: see text] is an independent variable, [Formula: see text] is an [Formula: see text] unknown variable matrix, [Formula: see text] and [Formula: see text] are given [Formula: see text] constant matrices, and [Formula: see text] is a given [Formula: see text] variable matrix. Under some commutativity conditions, a formula is derived for solving an initial problem [Formula: see text], [Formula: see text], where [Formula: see text] is an [Formula: see text] variable matrix. Previous results are discussed and open problems for further investigations suggested.