The Exponential Representation of Automorphs of a Symmetric or Hermitian Matrix

In a previous paper 1 the exponential representation of canonical matrices was studied. These canonical matrices are automorphs of the normal form of a skew symmetric matrix. The corresponding problem, when the skew symmetric matrix is replaced by a symmetric or hermitiani matrix, is considered here. Three cases are treated: when the matrix is symmetric over the complex field., when the matrix is hermitian, and when the matrix is symmetric over the real field. Of these three the last is by far the most interesting. The methods employed are similar to those of the paper quoted above and, as in many cases the proofs are practically identical, they will not always be given in detail.