Any way of adding vectors in a Hilbert space or multiplying them by scalars will yield a vector that is also in the space. In the case that the vector is normalized, it will, from (3.1), represent a possible state of the system, and in the event that it is the sum of a pair of eigenvectors of an observable \(B\) with distinct eigenvalues, it will not itself be an eigenvector of \(B\), but will be associated, from (3.4b), with a set of probabilities for showing one or another result in \(B\)-measurements.