  The random matrix ensembles are applied to the quantum statistical
two-dimensional systems of electrons. The quantum systems are studied using the
finite dimensional real, complex and quaternion Hilbert spaces of the
eigenfunctions. The linear operators describing the systems act on these
Hilbert spaces and they are treated as random matrices in generic bases of the
eigenfunctions. The random eigenproblems are presented and solved. Examples of
random operators are presented with connection to physical problems.
