Eigenvectors from eigenvalues: A survey of a basic identity in linear algebra
Eigenvectors from eigenvalues: A survey of a basic identity in linear algebra
If $A$ is an $n \times n$ Hermitian matrix with eigenvalues $\lambda _1(A),\dots ,$ $\lambda _n(A)$ and $i,j = 1,\dots ,n$, then the $j$th component $v_{i,j}$ of a unit eigenvector $v_i$ associated to the eigenvalue $\lambda _i(A)$ is related to the eigenvalues $\lambda _1(M_j),\dots ,$ $\lambda _{n-1}(M_j)$ of the minor …