Observables are represented by Hermitian operators. First of all, it's a little strange (to me) that some measurable physical quantity is represented by a transformation (or linear map), given that I think of a linear map as a function and I don't think of physical quantities as functions. But this is not my doubt. I try to accept this definition.
The resulting quantum state to which a system collapses after a measurement is one of the eigenvectors of this Hermitian operator. The corresponding eigenvalue is the result of the measurement.
If I understood correctly, a measurement is performed by a transformation, that is, in linear algebraic terms, you multiply by a matrix.
Anyway, I am not fully understanding the relation and connection between the measurement and an observable (or the Hermitian operator that represents it). How are measurements and observables in quantum mechanics related?