A matrix pair of an almost diagonal skew-symmetric matrix and a symmetric positive definite matrix
Copyright policy )A matrix pair of an almost diagonal skew-symmetric matrix and a symmetric positive definite matrix
Let A be skew-symmetric, B be symmetric positive definite, and the pair (A, B) have multiple eigenvalues. If A is close to Murnaghan form and B is close to diagonal form, then certain principal submatrices of A and B are specially related. In this paper we describe this relationship and quantify it under the usual asymptotic conditions. If B=I, the identity matrix, the result describes a special structure of a skew-symmetric matrix almost in Murnaghan form. We then briefly discuss how the Paardekooper method for skew-symmetric matrices asymptotically behaves in the presence of multiple eigenvalues.
- University of Zagreb Croatia
- University of Missouri–Kansas City United States
- University of Missouri United States
Numerical computation of eigenvalues and eigenvectors of matrices, Numerical Analysis, Eigenvalues, singular values, and eigenvectors, Algebra and Number Theory, skew-symmetric, symmetric positive definite, asymptotic behavior of diagonalization methods, Murnaghan form, quadratic convergence, generalized skew-symmetric eigenvalues problem, Paardekooper method, almost diagonal matrix pair, Discrete Mathematics and Combinatorics, Hermitian, skew-Hermitian, and related matrices, multiple eigenvalues, Geometry and Topology, Almost diagonal matrices; pair of a skew-symmetric and a positive definite matrix
Numerical computation of eigenvalues and eigenvectors of matrices, Numerical Analysis, Eigenvalues, singular values, and eigenvectors, Algebra and Number Theory, skew-symmetric, symmetric positive definite, asymptotic behavior of diagonalization methods, Murnaghan form, quadratic convergence, generalized skew-symmetric eigenvalues problem, Paardekooper method, almost diagonal matrix pair, Discrete Mathematics and Combinatorics, Hermitian, skew-Hermitian, and related matrices, multiple eigenvalues, Geometry and Topology, Almost diagonal matrices; pair of a skew-symmetric and a positive definite matrix
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