Professor Vector was the Arithmancy professor at Hogwarts. She had a reputation for being a strict teacher and was known to give a lot of complicated homework. Hermione Granger loved her class, but others were a bit less enthusiastic about taking Arithmancy from Vector (PA12, GF13, HBP24).
Vector (from mathematics): "quantity having both a number value and a direction."
Professor Vector's first name, Septima, appears on a list Jo created while planning Prisoner of Azkaban; however, her first name cannot be considered canon without further confirmation because other information on this page changed by the time the book was actually published (JKR scrapbook). Septima comes from "sept-", the Latin root for the number seven, very fitting for an arithmancer.
In the first film, Vector was played by Hazel Showham.