Weakly spectrally complete pair of matrices

Abstract

Let and be matrices over an algebraically closed field . Let be elements of such that and . We give necessary and sufficient condition for the existence of matrices and similar to and , respectively, such that has eigenvalues .

Keywords:

• eigenvalues
• invariant polynomials
• factorization of matrices

AMS Subject Classifications:

• 15A18
• 15A23

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research for this paper was done within the activities of Centro de Estruturas Lineares e Combinatórias da Universidade de Lisboa (CELC) and was partially supported by the Fundação para a Ciência e Tecnologia (Portugal).