On a formula of Thompson and McEnteggert for the adjugate matrix

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Date
2022
Author
Castillo, Kenier
Zaballa Tejada, Juan Bernardo ORCID
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Linear algebra and its applications 637 : 37-56 (2022)
URI
http://hdl.handle.net/10810/55472
Abstract
For an eigenvalue lambda(0) of a Hermitian matrix A, the formula of Thompson and McEnteggert gives an explicit expression of the adjugate of lambda I-0 - A, Adj(lambda I-0 - A), in terms of eigenvectors of Afor lambda(0) and all its eigenvalues. In this paper Thompson-McEnteggert's formula is generalized to include any matrix with entries in an arbitrary field. In addition, for any nonsingular matrix A, a formula for the elementary divisors of Adj(A) is provided in terms of those of A. Finally, a generalization of the eigenvalue-eigenvector identity and three applications of the Thompson-McEnteggert's formula are presented.
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Except where otherwise noted, this item's license is described as This article is available under the Creative Commons CC-BY-NC-ND license and permits non-commercial use of the work as published, without adaptation or alteration provided the work is fully attributed.