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• W3138597824 abstract "For an eigenvalue $lambda_0$ of a Hermitian matrix $A$, the formula of Thompson and McEnteggert gives an explicit expression of the adjoint of $lambda_0 I-A$, $mathrm{adj}(lambda_0 I-A)$, in terms of eigenvectors of $A$ for $lambda_0$ 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 $mathrm{adj}(A)$ is provided in terms of those of $A$. Finally, a generalization of the eigenvalue-eigenvector identity and two applications of the Thompson-McEnteggert's formula are presented." @default.
• W3138597824 created "2021-03-29" @default.
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• W3138597824 date "2021-03-25" @default.
• W3138597824 modified "2023-09-27" @default.
• W3138597824 title "On a formula of Thompson and McEnteggert for the adjugate matrix" @default.
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