Search results for "Matrix pencil"
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Spectral study of {R,s+1,k}- and {R,s+1,k,∗}-potent matrices
2020
Abstract The { R , s + 1 , k } - and { R , s + 1 , k , ∗ } -potent matrices have been studied in several recent papers. We continue these investigations from a spectral point of view. Specifically, a spectral study of { R , s + 1 , k } -potent matrices is developed using characterizations involving an associated matrix pencil ( A , R ) . The corresponding spectral study for { R , s + 1 , k , ∗ } -potent matrices involves the pencil ( A ∗ , R ) . In order to present some properties, the relevance of the projector I − A A # where A # is the group inverse of A is highlighted. In addition, some applications and numerical examples are given, particularly involving Pauli matrices and the quaterni…
Inversion of matrix pencils for generalized systems
1993
Abstract This paper clarifies the nature of the Leverrier-Faddeev algorithm for generalized and state-space systems. It presents useful diagrams for recursive computation of the coefficients of the characteristic polynomial and the coefficient matrices of the adjoint matrix for various matrix pencils. A simplified case covers recursive equations and diagrams for inversion of the second-order matrix pencil (Es2 + A1s + A0) where E may be singular. The appendix provides two examples of mechanical and heat exchange systems which can be described by the generalized models.