A note on group matrices
Olga Taussky · Proceedings of the American Mathematical Society · 1955
Let G be a finite group of order wwith elements P, Q, • • • .Let xp, xq, ■ • • hen indeterminates assumed in 1-1 correspondence with the elements of G. "The" group matrix corresponding to G is then the raXra matrix Oq-0, P,QGG.If numerical values are given to the x then we call the resulting matrix "a" group matrix.This note gives a new characterization of hamiltonian groups by means of group matrices.A matrix A of complex numbers is called normal if AA*=A*A where A* is the transposed, complex conjugate of A. If the matrix also contains indeterminates we introduce formally their conjugates and define normality as before.If the indeterminates are considered identical with their conjugates they are called real.