Some matrix factorization theorems. II
Robert Thompson · Pacific Journal of Mathematics · 1970
In the first part of this paper a thorough analysis was made of the matrix equation C = ABA^B' 1 when C, A, B are normal matrices.Not included, however, was the discussion of this equation when A and B are real skew-symmetric matrices.In the present paper we complete the investigation by giving this discussion.Throughout this paper we adopt the notation and terminology of part I.We also continue the convention that all matrices appearing in this paper, except the zero matrix, are to be nonsingular.We always let J£i, K 2 denote real skew symmetric matrices.LEMMA 1.Let M be a matrix with linear elementary divisors, and let M = K X K 2 be a product of two real skew-symmetric matrices K 19 K 2 .Then each eigenvalue of M has even multiplicity.