Septima Vector is the Arithmancy professor at Hogwarts School of Witchcraft and Wizardry. Professor Vector is female and likes to give her pupils plenty of complicated homework, yet she never speaks and only appears seldomly. This is possibly due to the fact that Harry Potter, as the title character, does not take Arithmancy, having chosen Divination instead (the two subjects share the same slot in his school timetable). Arithmancy is Hermione Granger's favourite subject, and it is mostly through her that we receive our impressions of Professor Vector. Alongside her colleague Professor Sinistra.
Septima most likely comes from the French Sept, which translates to "seven". As seven is the most powerful magical number, and Arithmancy deals with the numbers appearing in magic, it is very possible that her name originates from Sept. A "vector" is a quantity, velocity for instance, specified by a magnitude and a direction.