Hi, everyone, it's been a while!

I have a question about vectors.

Searching on internet for definition of vectors I often get that vectors are quantities with ability to represent magnitude and direction simultaneously.

In my math book there isn't definition of vectors, just explanation, but as I understand it, vectors are objects similar to sets or arrays, they can hold more elements then scalar quantities which are generaly numbers. So vectors can hold two or more numbers, lines, shapes or any math objects which are in specific relation.

Is my interpretation of vectors correct and can someone give me exact math definiton of vectors?