There has recently been an intense discussion about the (re)discovery of a formula that relates the components of an orthonormal basis of eigenvectors of an Hermitian matrix A of order n to the eigenvalues of A and the eigenvalues of some sub-matrices of A of order n -1. In this paper we will show that the above-mentioned formula is a consequence of the simultaneous diagonalization of a square matrix (not necessarily Hermitian) and its adjugate matrix.

Eigenvectors and eigenvalues: a new formula?

Alessandra Bertapelle
;
Maurizio Candilera
2020

Abstract

There has recently been an intense discussion about the (re)discovery of a formula that relates the components of an orthonormal basis of eigenvectors of an Hermitian matrix A of order n to the eigenvalues of A and the eigenvalues of some sub-matrices of A of order n -1. In this paper we will show that the above-mentioned formula is a consequence of the simultaneous diagonalization of a square matrix (not necessarily Hermitian) and its adjugate matrix.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3337785
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