PERTURBATION ANALYSIS OF THE EIGENVECTOR MATRIX AND SINGULAR VECTOR MATRICES

Let $A$ be an $n\times n$ Hermitian matrix and $A=U\Lambda U^H$ be its spectral decomposition, where $U$ is a unitary matrix of order $n$ and $\Lambda$ is a diagonal matrix. In this note we present the perturbation bound and condition number of the eigenvector matrix $U$ of $A$ with distinct eigenvalues. A perturbation bound of singular vector matrices is also given for a real $n\times n$ or $(n+1)\times n$ matrix. The results are illustrated by numerical examples.

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