The Conjunctive Equivalence of Pencils of Hermitian and Anti-Hermitian Matrices
John H. Williamson · American Journal of Mathematics · 1937
Let K be a commutative field of characteristic zero and let K (i) be a quadratic adjunction field of K, where i is a zero of the polynomial x2 a, irreducible in K. If A is a matrix with elements in K (i), or more shortly a matrix over K(i), the matrix A* is defined to be the conjugate transposed of A, so that A* A'. In particular, if A is a matrix over K, A* -A', the transposed of A. Let (1) A ==rA +sB,