The interpretation of the state vector, whose components are written ψ m, was furnished by Born. This interpretation is statistical: the result of a measurement of the physical quantity corresponding to the matrix A is random, with an average value equal to ∑ ∑ m n ψ ψ m ∗ ∗ A m n ψ ψ n . Alternatively, and equivalently, the state vector gives the probability amplitude ψ n for the quantum system to be in the energy state n.