Abstract
Canonical forms for matrix triples (A,G,(G) over cap), where A is arbitrary rectangular and G, (G) over cap 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.
| Original language | English |
|---|---|
| Pages (from-to) | 303-356 |
| Number of pages | 54 |
| Journal | Operators and Matrices |
| Volume | 3 |
| Issue number | 3 |
| Publication status | Published - 1 Sept 2009 |
Keywords
- indefinite inner product
- structured SVD
- Hamiltonian matrix
- skew-Hamiltonian matrix
- matrix triples
- canonical form