Eigenvectors from eigenvalues: A survey of a basic identity in linear algebra

Peter B. Denton, Stephen J. Parke, Terence Tao +1

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 $j^{\mathrm{th}}$ component $v_{i,j}$ of a unit eigenvector $v_i$…