Matriculation is the noun: the act, the moment, or the official process of starting at a university (or, in the US, a school or college). It is matriculate turned into a thing you can point at — after matriculation, she moved into halls. In some universities it is a ceremony. In others it is paperwork: your name is entered, you get a student number, you now have a place. Taiwan students already know this feeling as 註冊 and 取得學籍, even if nobody on campus says the English word. Though actually, the tidy university-start meaning is not the only one you will meet. In South Africa, India, and some older British use, matriculation (or matric) can mean the exam or certificate at the end of secondary school — the thing that lets you apply to university, not the university start itself. If you see the word, look at the country. And again, it is not graduation.