TY - GEN A1 - Mehl, Christian A1 - Mehrmann, Volker A1 - Xu, Hongguo T1 - Structured decompositions for matrix triples: SVD-like concepts for structured matrices N2 - Canonical forms for matrix triples $(A,G,\hat G)$, where $A$ is arbitrary rectangular and $G$, $\hat G$ are either real symmetric or skew symmetric, or complex Hermitian or skew Hermitian, are derived. These forms generalize classical product Schur forms as well as singular value decompositions. An new proof for the complex case is given, where there is no need to distinguish whether $G$ and $\hat G$ are Hermitian or skew Hermitian. This proof is independent from the results in Bolschakov/Reichstein 1995, where a similar canonical form has been obtained for the complex case, and it allows generalization to the real case. Here, the three cases, i.e., that $G$ and $\hat G$ are both symmetric, both skew symmetric or one each, are treated separately. KW - Matrix triples KW - indefinite inner product KW - structured SVD KW - canonical form KW - Hamiltonian matrix KW - skew-Hamiltonian matrix Y1 - 2008 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/521 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-5210 ER -