Let A be a normal n×n matrix. This paper discusses in detail under what conditions and in what way A can be dilated to a normal matrix of order n+1 or n+2. Bibliography: 4 titles.

Abstract Two square complex matrices A , B are said to be unitarily congruent if there is a unitary matrix U such that A = UBU T . The Youla form is a canonical form under unitary congruence. We… Expand

Conjugate-normal matrices play the same important role in the theory of unitary congruence as the conventional normal matrices do with respect to unitary similarities. However, unlike the latter, the… Expand

Abstract Recently, H. Fassbender et al. [Linear Algebra Appl. 287 (1999) 125] proved the following theorem: Every real skew-Hamiltonian matrix W has a real Hamiltonian square root H, i.e., H 2 =W. We… Expand

An algorithm of the Bartels-Stewart type for solving the matrix equation AX + XTB = C is proposed. By applying the QZ algorithm, the original equation is reduced to an equation of the same type… Expand