Eigenvectors from eigenvalues: A survey of a basic identity in linear algebra
Peter Denton, Stephen Parke, Terence Tao, Xining Zhang · Bulletin of the American Mathematical Society · 2021
If A A is an n × n n \times n Hermitian matrix with eigenvalues λ 1 ( A ) , … , \lambda _1(A),\dots , λ n ( A ) \lambda _n(A) and i , j = 1 , … , n i,j = 1,\dots ,n , then the j j th component v i , j v_{i,j} of a unit eigenvector v i v_i associated to the eigenvalue λ i ( A ) \lambda _i(A) is related to the eigenvalues λ 1 ( M j ) , … , \lambda _1(M_j),\dots , λ n − 1 (