# Rayleigh-Ritz Theorem

1. ### S_David

601
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