Matsuda Nagahide is the elder and one of the four samurais in the Matsuda Clan. He has served as a kendo instructor for the Hojo Clan for many years already. Hojo Ujizane was also one of his disciples.
He is a pretty uptight and old-fashioned person, but that isn't necessarily a bad thing for Kagami Lily as he tend to maintain a certain distance from her.