On characteristic invariants of matrix pencils and linear relations

2022/03/15 by Hannes Gernandt, Francisco Martínez Pería, Gernandt, Hannes +5 · 1 citation
Computer Science · Engineering · Mathematics · #15A21 #15A22 #47A06 #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Spectral Theory (math.SP) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2203.08296

openalex publication_date 2022/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The relationship between linear relations and matrix pencils is investigated. Given a linear relation, we introduce its Weyr characteristic. If the linear relation is the range (or the kernel) representation of a given matrix pencil, we show that there is a correspondence between this characteristic and the Kronecker canonical form of the pencil. This relationship is exploited to obtain estimations on the invariant characteristics of matrix pencils under rank one perturbations.

Cited by

• Bounds for the change of the Weyr characteristic of matrix pencils after 1-rank perturbations

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