MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

2 corrected English technical term

A really elementary one :

A linear application map between two vector spaces of the same finite dimension is an isomorphism if and only if its kernel is zero.

As an application, I like the proof of the existence of Lagrange interpolation polynomials.