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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