STRUCTURED TOOLS FOR STRUCTURED MATRICES
By D. Steven Mackey, Niloufer Mackey, Françoise Tisseur. 2003
69 citations recorded by the source corpus.
An extensive and unified collection of structure-preserving transformations is pre- sented and organized for easy reference. The structures involved arise in the context of a non- degenerate bilinear or sesquilinear form on R n or C n . A variety of transformations belonging to the automorphism groups of these forms, that imitate the action of Givens rotations, Householder reflec- tors, and Gauss transformations are constructed. Transformations for performing structured scaling actions are also described. The matrix groups considered in this paper are the complex orthogonal, real, complex and conjugate symplectic, real perplectic, real and complex pseudo-orthogonal, and pseudo-unitary groups. In addition to deriving new transformations, this paper collects and unifies existing structure-preserving tools.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Spectroscopy
View Paper: https://www.semanticscholar.org/paper/a60cdf190adc69a471c26fd4d6c1c7d9b7db4fa6
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Citations in the corpus
- Neurobiology of Aging: Contents (2005, unknown): “Finally we mention that in most applications n is larger than m, often much larger.”
- Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory (2005, background): “Some additional groups of structured matrices are given in [386].”