specific observable on some and measurement of another observable on the rest, the statistical distributions of results in both series of measurements may or may not be correlated (non-commuting or commuting variables, respectively).

It is when non-commuting observables enter the picture that Planck’s universal constant $\hbar$ appears and delimits the “size” of the quantum domain. Historically, it was the position and the momentum of a particles which led Heisenberg to his uncertainty relationship between their standard deviations in measurements under similar conditions ($\Delta x \Delta p \ge {\hbar} /2$). For the sake of completeness of this summary, we must also mention that Schrödinger’s equation is introduced when the time evolution of a quantum system is to be described (which, however, will not be dealt with in this article).

All these experimental facts indeed allow the development of linear algebra algorithms in which general states of a quantum system (those which, when measured under equal conditions, give different results from among a set of eigenvalues) are represented by (unit) vectors in a Hilbert space; interactions such as measurements and transformations (e.g., mutual interactions, time evolution) are represented by specific operators. Each observable defines a subspace whose axes represent its eigenstates or 