TY - GEN A1 - Mehl, Christian A1 - Mehrmann, Volker A1 - Xu, Hongguo T1 - Singular-value-like decomposition for complex matrix triples N2 - The classical singular value decomposition for a matrix $A\in\Cmn$ is a canonical form for $A$ that also displays the eigenvalues of the Hermitian matrices $AA^\ast$ and $A^\ast A$. In this paper, we develop a corresponding decomposition for $A$ that provides the Jordan canonical forms for the complex symmetric matrices $AA^T$ and $A^TA$. More generally, we consider the matrix triple $(A,G_1,G_2)$, where $G_1\in\CC{m}, G_2\in\CC{n}$ are invertible and either complex symmetric and complex skew-symmetric, and we provide a canonical form under transformations of the form $(A,G_1,G_2)\mapsto(X^T A Y, X^T G_1X, Y^T G_2Y)$, where $X,Y$ are nonsingular. KW - ingular value decomposition KW - canonical form KW - complex bilinear forms KW - complex symmetric matrix KW - complex skew-symmetric matrix KW - Hamiltonian matrix KW - Takagi factorization Y1 - 2007 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/422 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-4224 ER -