This article studies an analog of the classical eigenvalue–eigenvector identity for dual Hermitian matrices. The classical identity relates the eigenvalues of a Hermitian matrix, the eigenvalues of its principal submatrices, and the entries of its eigenvectors. Assuming that the standard eigenvalues are simple, we establish the corresponding identity for dual Hermitian matrices and show that it naturally decomposes into a standard component and a dual component. The standard component recovers the classical Hermitian identity, while the dual component yields an explicit first-order correction formula relating eigenvalue and eigenvector corrections to perturbations of the corresponding principal submatrices. Numerical examples are presented to verify the theoretical results.
