LU decomposition and generalized Autoone-Takagi decomposition of dual matrices and their applications
Renjie Xu, Yimin Wei, Yan Hong
Abstract
This paper uses matrix transformations to provide the Autoone-Takagi decomposition of dual complex symmetric matrices and extends it to dual quaternion η-Hermitian matrices. The LU decomposition of dual matrices is given using the general solution of the Sylvester equation, and its equivalence to the existence of rank-k decomposition and dual Moore-Penrose generalized inverse (DMPGI) is proved. Similar methods are then used to provide the Cholesky decomposition of dual real symmetric positive definite matrices. Both of our decompositions are driven by applications in numerical linear algebra.
Topics & Concepts
DecompositionDual (grammatical number)MathematicsMatrix decompositionComputer scienceChemistryPhysicsPhilosophyLinguisticsEigenvalues and eigenvectorsOrganic chemistryQuantum mechanicsMatrix Theory and AlgorithmsWireless Communication Networks ResearchAdvanced MIMO Systems Optimization