# Algebraic and geometric multiplicities

I'm aware of the formal definition of algebraic and geometric multiplicities, but I can't make much sense out of the names.

What I mean is, if it were me, I would name these two quantities multiplicity one and multiplicity two, for all I know. But I'm guessing that the people who named these two quantities had something intuitive in mind when they defined them as algebraic and geometric. Is it just because the first is referring to a polynomial (which is kind of algebraic) and the second to a dimension (which is kind of geometric), or is it something more profound that I'm missing?

• Thanks for the title and tags editing to k170, will keep the idea in mind in future posts. – Martín Forsberg Conde Dec 8 '15 at 16:40