Canonical forms for normal matrices that commute with their complex conjugate (Q999786)

The authors continue their previous work [cf. \textit{G. R. Goodson, R. A. Horn} and \textit{D. I. Merino}, Linear Algebra Appl. 369, 279--294 (2003; Zbl 1024.15005)]. They consider the class of normal complex matrices that commute with their complex conjugates. They show that such matrices are real orthogonally similar to a canonical direct sum of 1-by-1 and certain 2-by-2 matrices. A canonical form for quasi-real normal matrices is obtained as a special case. The paper also exhibits a special form of the spectral theorem for normal matrices that commute with their conjugate.