# Rayleigh-Ritz Theorem

by S_David
Tags: rayleighritz, theorem
 P: 597 Hi, I have the following $$\underset{\|\mathbf{x}\|^2=1}{\text{max }}\mathbf{x}^{H}\mathbf{A}^{-1}\mathbf{x}=\lambda_{\text{max}}\left(\mathbf{A^{-1}}\right)$$ which is the maximum singular value of the inverse of a diagonal matrix A. Now does this equivalent to $$\lambda_{\text{min}}\left(\mathbf{A}\right)$$ which is the minimum singular value of the matrix A? Thanks