Główne pojęcia
Practical method using supplement matrices to compute eigenvalues of dual Hermitian matrices.
Streszczenie
The study focuses on dual number symmetric matrices, dual complex Hermitian matrices, and dual quaternion Hermitian matrices within the framework of dual Hermitian matrices. The article introduces supplement matrices for a dual Hermitian matrix, which are Hermitian matrices in the original ring. By utilizing practical methods for computing eigenvalues of standard part Hermitian matrices in the original ring, a practical method is established for computing eigenvalues of a dual Hermitian matrix. Applications in low rank approximation, generalized inverses of dual matrices, least squares problems, and formation control are discussed with reported numerical experiments.
Statystyki
An n × n dual quaternion Hermitian matrix has n dual number eigenvalues.
Several numerical methods for computing eigenvalues of dual quaternion Hermitian matrices include a power method, bidiagonalization method, and Rayleigh quotient iteration method.
A unitary matrix V and U exist such that V ∗AU = Σt O O O where Σt is a diagonal matrix with appreciable and infinitesimal singular values.
Cytaty
"The standard parts of the eigenvalues of that dual Hermitian matrix are the eigenvalues of the standard part Hermitian matrix in the original ring."
"Applications to low rank approximation and generalized inverses of dual matrices, dual least squares problem and formation control are discussed."
"We call this method the supplement matrix method."