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arXiv · 2301.13548

Structure-preserving eigenvalue modification of symplectic matrices and matrix pencils

Philip Saltenberger
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Abstract

A famous theorem by R. Brauer shows how to modify a single eigenvalue of a matrix by a rank-one update without changing the remaining eigenvalues. A generalization of this theorem (due to R. Rado) is used to change a pair of eigenvalues of a symplectic matrix S in a structure-preserving way to desired target values. Universal bounds on the relative distance between S and the newly constructed symplectic matrix S' with modified spectrum are given. The eigenvalues Segre characteristics of S' are related to those of S and a statement on the eigenvalue condition numbers of S' is derived. The main results are extended to matrix pencils.

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Philip Saltenberger. 2023-01-31. Structure-preserving eigenvalue modification of symplectic matrices and matrix pencils. https://arxiv.org/abs/2301.13548

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