Structured decompositions for matrix triples: SVD-like concepts for structured matrices
Christian Mehl, Volker Mehrmann, Hongguo Xu · Operators and Matrices · 2009
Canonical forms for matrix triples (A,G, ) , where A is arbitrary rectangular and G , are either real symmetric or skew symmetric, or complex Hermitian or skew Hermitian, are derived. These forms generalize classical singular value decompositions. In [1] a similar canonical form has been obtained for the complex case. In this paper, we provide an alternative proof for the complex case which is based on the construction of a staircase-like form with the help of a structured QR -like decomposition. This approach allows generalization to the real case.