There was an ancient literary Pyrrhus, son of Achilles, who took Andromache, wife of Hector, as part of his spoils from the Trojan War and had three sons by her. One of these sons became king of Epirus after Pyrrhus' death.
We know little else about this Pyrrhus, however, and Racine has based Pyrrhus' character here on what would be expected from a son of Achilles — that same Achilles who sulked in his tent when his captive was taken from him and almost allowed the Greeks to lose the Trojan War. Like Achilles, Pyrrhus is violent and hot-tempered and puts his own passions above the interests of the Greek states. His chief traits are arrogance and impatience.
Nevertheless, he is brave and faithful to his word and ultimately protects Andromache's son at the cost of his own safety. He is capable of love, however imperious and self-centered that love may be; he loves a woman who is herself admirable, and he seems quite indifferent to the fact that she is a slave and an enemy. Moreover, toward the end of the play, he seems to be acquiring a dim awareness that following the dictates of one's own will may involve unexpected responsibilities and penalties, and he is prepared to accept these. Pyrrhus is a barbarian, but not an ignoble one.