  A general framework for the description of the physical properties of matter
by a canonical reduction procedure of tensors is presented; besides geometrical
symmetries, this paper emphasizes the role of intrinsic symmetries which are
due either to the indiscernability of some of the physical quantities involved
or to thermodynamical arguments. The intrinsic symmetries are expressed through
the behaviour of the tensors describing the investigated property under the
effect of some index permutation. The scheme of reduction of any tensor into
parts that are irreducible not only with respect to rotations and inversion but
also with respect to index permutations is shown and examples are given in the
area of light-matter interaction.
