On the Symmetry Point Groups for Some Simple Parameter-Dependent Symmetric Matrices

We try to determine the groups of orthogonal matrices that commute with a given simple parameter-dependent symmetric matrix. To this end we resort to a graphical representation of the latter that enables us to find the group of matrices from the symmetry elements of the figure. This strategy works fine for all values of the model parameter λ except for λ = −1. In order to obtain the symmetry point group in this particular case we have to resort to alternative procedures.